Search results for: formal proof

Authors: Yingxu Wang

Abstract:

The base 6 structure and properties of mirror primes are discovered in this work towards the proof of Goldbach Conjecture. This paper reveals a fundamental pattern on pairs of mirror primes adjacent to any even number nₑ > 2 with symmetrical distances on both sides determined by a methodology of Mirror Prime Decomposition (MPD). MPD leads to a formal proof of the Goldbach conjecture, which states that the conjecture holds because any pivot even number, nₑ > 2, is a sum of at least an adjacent pair of primes divided by 2. This work has not only revealed the analytic pattern of base 6 primes but also proven the infinitive validation of the Goldbach conjecture.

Keywords: number theory, primes, mirror primes, double recursive patterns, Goldbach conjecture, formal proof, mirror-prime decomposition, applications

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Authors: Yingxu Wang

Abstract:

This work presents basic research on the recursive structures and dual sequential patterns of primes for the formal proof of the Twin-Prime Conjecture (TPC). A rigorous methodology of Twin-Prime Decomposition (TPD) is developed in MATLAB to inductively verify potential twins in the dual sequences of primes. The key finding of this basic study confirms that the dual sequences of twin primes are not only symmetric but also infinitive in the unique base 6 cycle, except a limited subset of potential pairs is eliminated by the lack of dual primality. Both theory and experiments have formally proven that the infinity of twin primes stated in TPC holds in the P x P space.

Keywords: number theory, primes, twin-prime conjecture, dual primes (P x P), twin prime decomposition, formal proof, algorithm

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Authors: Rahmayanti, Theresia Simatupang, Ronald H. Sianturi

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Corruption criminal act develops rapidly since in the transition era there is weakness in law. Consequently, there is an opportunity for a few people to do fraud and illegal acts and to misuse their positions and formal functions in order to make them rich, and the criminal acts are done systematically and sophisticatedly. Some people believe that legal provisions which specifically regulate the corruption criminal act; namely, Law No. 31/1999 in conjunction with Law No. 20/2001 on the Eradication of Corruption Criminal Act are not effective any more, especially in onus probandi (the burden of proof) on corruptors. The research was a descriptive analysis, a research method which is used to obtain description on a certain situation or condition by explaining the data, and the conclusion is drawn through some analyses. The research used judicial normative approach since it used secondary data as the main data by conducting library research. The system of the burden of proof, which follows the principles of reversal of the burden of proof stipulated in Article 12B, paragraph 1 a and b, Article 37A, and Article 38B of Law No. 20/2001 on the Amendment of Law No. 31/1999, is used only as supporting evidence when the principal case is proved. Meanwhile, how to maximize the implementation of the burden of proof on the perpetrators of corruption criminal act in which the public prosecutor brings a corruption case to Court, depends upon the nature of the case and the type of indictment. The system of burden of proof can be used to eradicate corruption in the Court if some policies and general principles of justice such as independency, impartiality, and legal certainty, are applied.

Keywords: burden of proof, perpetrator, corruption criminal act

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Authors: Sakshi Singh, Shampa Chakraverty

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One of the essential characteristics of Blockchain is the ability to validate the integrity of new transactions added to the Blockchain. Moreover, one of the essential consensus algorithms, Proof of Work, performs this job. In this work, we implemented the Proof of Work consensus method on the block formed by performing the transaction using Ganache. The primary goal of this implementation is to understand the process and record how Proof of Work works in reality on newly created blocks.

Keywords: proof of work, blockchain, ganache, smart contract

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Authors: Rajaa Filali, Mohamed Bouhdadi

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This paper presents an incremental formal development of the Wireless Transaction Protocol (WTP) in Event-B. WTP is part of the Wireless Application Protocol (WAP) architectures and provides a reliable request-response service. To model and verify the protocol, we use the formal technique Event-B which provides an accessible and rigorous development method. This interaction between modelling and proving reduces the complexity and helps to eliminate misunderstandings, inconsistencies, and specification gaps. As result, verification of WTP allows us to find some deficiencies in the current specification.

Keywords: event-B, wireless transaction protocol, proof obligation, refinement, Rodin, ProB

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Authors: Soheib Fergani

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This paper concerns with the formal asymptotic stability guarantees, analysis and evaluation of a nonlinear controlled unmanned aerial vehicles (uav) for trajectory tracking purpose. As the system has been recognised as an under-actuated non linear system, the control strategy has been oriented towards a hierarchical control. The dynamics of the system and the mission purpose make it mandatory to provide an absolute proof of the vehicle stability during the maneuvers. For this sake, this work establishes the complete theoretical proof for an implementable control oriented strategy that asymptotically stabilizes (GAS and LISS) the system and has never been provided in previous works. The considered model is reorganized into two partly decoupled sub-systems. The concidered control strategy is presented into two stages: the first sub-system is controlled by a nonlinear backstepping controller that generates the desired control inputs to stabilize the second sub-system. This methodology is then applied to a harware in the loop uav simulator (SiMoDrones) that reproduces the realistic behaviour of the uav in an indoor environment has been performed to show the efficiency of the proposed strategy.

Keywords: UAV application, trajectory tracking, backstepping, sliding mode control, input to state stability, stability evaluation

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Authors: Frode van der Laak

Abstract:

The paper contributes to the feasibility of using a 5G mobile connection as a node for a Proof of Authority (PoA) blockchain, which is used for microtransactions at the same time. It uses the phone number identity of the users that are linked to the crypto wallet address. It also proposed a consensus protocol based on Proof-of-Authority (PoA) blockchain; PoA is a permission blockchain where consensus is achieved through a set of designated authority rather than through mining, as is the case with a Proof of Work (PoW) blockchain. This report will first explain the concept of a PoA blockchain and how it works. It will then discuss the potential benefits and challenges of using a 5G mobile connection as a node in such a blockchain, and finally, the main open problem statement and proposed solutions with the requirements.

Keywords: 5G, mobile, connection, node, PoA, blockchain, microtransaction

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Authors: Rajaa Filali, Mohamed Bouhdadi

Abstract:

This paper presents an incremental development of the Dynamic Host Configuration Protocol (DHCP) in Event-B. DHCP is widely used communication protocol, which provides a standard mechanism to obtain configuration parameters. The specification is performed in a stepwise manner and verified through a series of refinements. The Event-B formal method uses the Rodin platform to modeling and verifying some properties of the protocol such as safety, liveness and deadlock freedom. To model and verify the protocol, we use the formal technique Event-B which provides an accessible and rigorous development method. This interaction between modelling and proving reduces the complexity and helps to eliminate misunderstandings, inconsistencies, and specification gaps.

Keywords: DHCP protocol, Event-B, refinement, proof obligation, Rodin

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Authors: Osman Okumuş

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The pandemic has significantly affected every aspect of life. Especially in recenttimes, as a result of this effect, we have come closer to technology. Distance education has taken the place of formal education rather than supporting formal education. Thiscreatednewexperiencesforbothteachersandstudents. This research focused on revealing the experiences of the same students in distance and formal education, especially in history lessons. In the study, which was designed as a case study, 20 students were interviewed through a semi-structured interview form prepared by the researcher. The results show that both learning environments provide students with important experiences. However, despite the fact that the students developed their digital competencies and experienced different learning environments, they focused on formal education in the name of socialization.

Keywords: history lessons, distance education, pandemic., formal education

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Authors: Ying Yi Wu

Abstract:

In this paper, we present a proof of the fact that a finite morphism is proper. We show that a finite morphism is universally closed and of finite type, which are the conditions for properness. Our proof is based on the theory of schemes and involves the use of the projection formula and the base change theorem. We first show that a finite morphism is of finite type and then proceed to show that it is universally closed. We use the fact that a finite morphism is also an affine morphism, which allows us to use the theory of coherent sheaves and their modules. We then show that the map induced by a finite morphism is flat and that the module it induces is of finite type. We use these facts to show that a finite morphism is universally closed. Our proof is constructive, and we provide details for each step of the argument.

Keywords: finite, morphism, schemes, projection.

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Authors: Zulaiha Maluma Ahmad

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This paper attempted to examine adult and non formal education for the attainment of entrepreneurial skills in empowering the citizens with entrepreneurial skills, for Nigeria’s socioeconomic development. This paper highlighted the meaning of education in the context of skill acquisition, entrepreneurial education, adult and non formal education. It also examined the objectives, issues and challenges as well as prospects of this type of education. It further discussed the role of adult and non formal education for the attainment of socioeconomic development of a growing nation like Nigeria. The paper equally proffered some recommendations and eventually concluded that adult and non formal education can indeed make self reliance, personal satisfaction and the attainment of entrepreneurial education for the socioeconomic development of any nation, possible.

Keywords: entrepreneurial education, adult education, non formal education skills, Nigeria

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Authors: Jawid Ahmad Baktash, Mursal Dawodi, Tomokazu Nagata

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With the rapid growth of Cloud Computing, Formal Methods became a good choice for the refinement of message specification and verification for Dynamic Routing in Cloud Computing. Cloud-based Dynamic Routing is becoming increasingly popular. We propose feedback in Formal Methods for Dynamic Routing and Cloud Computing; the model and topologies show how to send messages from index zero to all others formally. The responsibility of proper verification becomes crucial with Dynamic Routing in the cloud. Formal Methods can play an essential role in the routing and development of Networks, and the testing of distributed systems. Event-B is a formal technique that consists of describing the problem rigorously and introduces solutions or details in the refinement steps. Event-B is a variant of B, designed for developing distributed systems and message passing of the dynamic routing. In Event-B and formal methods, the events consist of guarded actions occurring spontaneously rather than being invoked.

Keywords: cloud, dynamic routing, formal method, Pro-B, event-B

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Authors: Xia Yang, Zheng Yang, Haiyong Sun, Yan Fang, Jingyu Liu, Jia Song

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The smart contract in Ethereum is a unique program deployed on the Ethereum Virtual Machine (EVM) to help manage cryptocurrency. The security of this smart contract is critical to Ethereum’s operation and highly sensitive. In this paper, we present a formal model for smart contract, using the separated term-obligation (STO) strategy to formalize and verify the smart contract. We use the IBM smart sponsor contract (SSC) as an example to elaborate the detail of the formalizing process. We also propose a formal smart sponsor contract model (FSSCM) and verify SSC’s security properties with an interactive theorem prover Coq. We found the 'Unchecked-Send' vulnerability in the SSC, using our formal model and verification method. Finally, we demonstrate how we can formalize and verify other smart contracts with this approach, and our work indicates that this formal verification can effectively verify the correctness and security of smart contracts.

Keywords: smart contract, formal verification, Ethereum, Coq

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Authors: Wiem Gadri

Abstract:

This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

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Authors: Surinder Sood, Debajyoti Mukherjee

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Formal verification techniques have become widely popular in pre-silicon verification as an alternate to constrain random simulation based techniques. This paper proposed a novel formal verification-based coverage augmentation technique in verifying complex RTL functional verification faster. The proposed approach relies on augmenting coverage analysis coming from simulation and formal verification. Besides this, the functional qualification framework not only helps in improving the coverage at a faster pace but also aids in maturing and qualifying the formal verification infrastructure. The proposed technique has helped to achieve faster verification sign-off, resulting in faster time-to-market. The design picked had a complex control and data path and had many configurable options to meet multiple specification needs. The flow is generic, and tool independent, thereby leveraging across the projects and design will be much easier

Keywords: COI (cone of influence), coverage, formal verification, fault injection

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Authors: Chanoknart Mayusoh

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The research about Formal Thai National Costume in the reign of King Bhumibol Adulyadej is an applied research that aimed to study the accurate knowledge concerning to Thai national costume in the reign of King Rama IX, also to study origin of all costumes in the reign of King Rama IX and to study the style, material used, and using accasion. This research methodology which are collect quanlitative data through observation, document, and photograph from key informant of costume in the reign of King Rama IX and from another who related to this field. The formal Thai national costume of the reign of King Bhumibol Adulyadej originated from the visit of His Majesty the King to Europe and America in 1960. Since Thailand had no traditional national costume; Her Majesty the Queen initiated the idea to create formal Thai national costumes. In 1964, Her Majesty the Queen selected 8 styles of formal Thai national costume. Later, Her Majesty the Queen confered another 3 formal Thai national costume for men. There are 8 styles of formal Thai national costume for women: Thai Ruean Ton, Thai Chit Lada, Thai Amarin, Thai Borom Phiman, Thai Siwalia, Thai Chakkri, Thai Dusit, and Thai Chakkraphat. There are 3 styles of formal Thai national costume for men: short-sleeve shirt, long-sleeve shirt, and long-sleeve shirt with breechcloth. The costume is widely used in formal ceremony such as greeting ceremony for official foreign visitors, wedding ceremony, or other auspicious ceremonies. Now a day, they are always used as a bridal gown as well. The formal Thai national costume is valuable art that shows Thai identity and, should be preserved for the next generation.

Keywords: formal Thai national costume for women, formal Thai national costume for men, His Majesty King Bhumibol Adulyadej the Great King Rama IX, Her Majesty Queen Sirikit Queen

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Authors: Minh Thi Hai Vo

Abstract:

This article draws on in-depth interviews with state employees at public hospitals and universities in its institutional analysis of the autonomy practices of public service delivery units in Vietnam. Unlike many empirical and theoretical studies that view formal and informal institutions as complements or substitutes, this article finds no evidence of complementary or substitutive relationships. Instead, the article finds that formal institutions accommodate informal ones and that informal institutions tend to compete and interfere, with the existing and ineffective formal institutions. The result of such conflicting relationship is that the actual autonomy of public service delivery units is, in most cases, perceived to be greater than the formal autonomy they are given. In the condition of poor regulation, the informal autonomy may result in unethical practices including rent-seeking and corruption. The implication of the study finding is policy-makers need to redesign and reorganize the autonomisation of public service delivery units to make informal institutions support and reinforce formal ones in a complementary manner.

Keywords: autonomy, formal institutions, informal institutions, public service delivery units, Vietnam

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Authors: Leilei Liang

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Leadership is commonly classified as formal leadership and informal leadership, which ignores and neglects the effects of 3rd type leadership. The emergence of 3rd type of leadership is closely related to special relations. To figure out the mechanism and effects of 3rd type leadership as well as the impacts of formal leadership and informal leadership on employee performance, this study collects data from 350 participants through a survey and proposes three hypotheses respectively from the perspective of expectation theory. The analytical results provide strong evidence for two of the three hypotheses, which demonstrate the positive correlation between formal leadership and individual performance and the negative relationship between 3rd type leadership and individual performance. This study contributes to leadership literature by putting forward the concept of the 3rd type of leadership. In addition, the effects of formal leadership, informal leadership, and 3rd type leadership on individual performance are discussed respectively in this study.

Keywords: formal leadership, informal leadership, 3rd leadership, individual performance, expectation theory

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Authors: Feng-Hisang Lai

Abstract:

CFD(Computational Fluid Dynamics) is conducted to numerically study the flow and heat transfer features of a two-pole, 6,080HP, 60Hz, 3,150V open drip-proof (ODP) motor. The stator and rotor cores in this high voltage induction motor are segmented with the use of spacers for cooling purposes, which leads to difficulties in meshing when the entire system is to be simulated. The system is divided into 4 parts, meshed separately and then combined using interfaces. The deviation between the CFD and experimental results in temperature and flow rate is less than 10%. The internal flow is further examined and a final design is proposed to reduce the winding temperature by 10 degrees.

Keywords: CFD, open drip proof, induction motor, cooling

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Authors: Lei Zhang, Li Ji

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Formal learning and informal learning represent two distinct learning styles: one is systematic and organized, another is causal and unstructured. Although there are many factors influencing online learning satisfaction, including self-regulation, self-efficacy, and interaction, factors influencing online formal learning and informal learning satisfaction may differ from each other. This paper investigated and compared influential factors of online formal and informal learning. Two questionnaires were created based on previous studies to explore factors influencing online formal learning and online informal learning satisfaction, respectively. A sample of 105 college students from different departments in a university located in the eastern part of China was selected to participate in this study. They all had an online learning experience and agreed to fill out questionnaires. Correlation analysis, variance analysis, and regression analysis were employed in this study. In addition, five participants were chosen for interviews. The study found that student-content, interaction, self-regulation, and self-efficacy related positively to both online formal learning and informal learning satisfaction. In addition, compared to online formal learning, student-content interaction in informal learning was the most influential factor for online learning satisfaction, perhaps that online informal learning was more goal-oriented and learners paid attention to the quality of content. In addition, results also revealed that interactions among students or teachers had little impact on online informal learning satisfaction. This study compared influential factors in online formal and informal learning satisfaction helped to add discussions to online learning satisfaction and contributed to further practices of online learning.

Keywords: learning satisfaction, formal learning, informal learning, online learning

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Authors: Rabinder Singh Bharj, Sandeep Kumar

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This investigation presents preparation of sample and analysis of results of ballistic impact test as per EN 1063 on the size, thickness, number, position, and type of the bonding interlayer Polyvinyl Butyral, Poly Carbonate and Poly Urethane on bullet proof glass. It was observed that impact energy absorbed by bullet proof glass increases with the increase of the total thickness from 33mm to 42mm to 51mm for all the three samples respectively. Absorption impact energy is greater for samples with more number of bonding interlayers than with the number of glass layers for uniform increase in total sample thickness. There is no effect on the absorption impact energy with the change in position of the bonding interlayer.

Keywords: absorbed energy, bullet proof glass, laminated glass, safety glass

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Authors: Ahmed Tarek, Ahmed Alveed

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In the theory of computing, there are a wide variety of direct and indirect proof techniques. However, mathematical induction (MI) stands out to be one of the most powerful proof techniques for proving hypotheses, theorems, and new results. There are variations of mathematical induction-based proof techniques, which are broadly classified into three categories, such as structural induction (SI), weak induction (WI), and strong induction (SI). In this expository paper, several different variants of the mathematical induction techniques are explored, and the specific scenarios are discussed where a specific induction technique stands out to be more advantageous as compared to other induction strategies. Also, the essential difference among the variants of mathematical induction are explored. The points of separation among mathematical induction, recursion, and logical deduction are precisely analyzed, and the relationship among variations of recurrence relations, and mathematical induction are being explored. In this context, the application of recurrence relations, and mathematical inductions are considered together in a single framework for codewords over a given alphabet.

Keywords: alphabet, codeword, deduction, mathematical, induction, recurrence relation, strong induction, structural induction, weak induction

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Authors: Gyoutae Park, Seungho Han, Byungduk Kim, Youngdo Jo, Yongsop Shim, Yeonjae Lee, Sangguk Ahn, Hiesik Kim, Jungil Park

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In this paper, we presented not only development technology of an explosion proof type and portable combustible gas leak detector but also algorithm to improve accuracy for measuring gas concentrations. The presented techniques are to apply the flame-proof enclosure and intrinsic safe explosion proof to an infrared gas leak detector at first in Korea and to improve accuracy using linearization recursion equation and Lagrange interpolation polynomial. Together, we tested sensor characteristics and calibrated suitable input gases and output voltages. Then, we advanced the performances of combustible gaseous detectors through reflecting demands of gas safety management fields. To check performances of two company's detectors, we achieved the measurement tests with eight standard gases made by Korea Gas Safety Corporation. We demonstrated our instruments better in detecting accuracy other than detectors through experimental results.

Keywords: accuracy improvement, IR gas sensor, gas leak, detector

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Authors: Sumaira Saleem

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This study reveals that the use of SMS effect the formal writing of the students. SMS is in vogue sine the last decade but its detrimental effects are effecting not only to the set norms but also deviant forms of expressions have come into the community to which all are not acquainted and it creates a hurdle in effective communication. It also determines the reasons behind the usage of SMS practices in the formal writings like in assignments and examinations. For this study a questionnaire was designed for faculty and students the data was collected from The Islamia University Bahawalpur and the formal work of the students was also collected to check the manifestation of SMS practices in writings. Data was analysed on excel sheet and the tables and graphs are used to explain the ratios and percentages of SMS usage. The results show that the usage of SMS has very strong effect upon the students writing.

Keywords: technology, writing, effects, SMS

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Authors: Mirza Amin Ul Haq

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Purpose – the purpose of conducting this research is to check the impact of nudges constructs, whether they create an encouragement factor with consumer brand loyalty and relating of word-of-mouth power have some kind of effect with all independent variables. Desin/Methodology/Approach – this study adopted the four constructs (i.e., Digital Nudge, Social Proof Nudge, Trust, and the mediator Word of Mouth) and explore its effect and connection with Brand Loyalty. A total of 390 respondents were selected for self-administrated questionnaire to obtain the finding of the research. Findings – the impact and cause between the constructs were done through structural equation modeling. The findings show a positive impact of social proof nudge and word of mouth whereas, digital nudge and trust have the weaker influence on the consumer choices when talk about brand loyalty. Originality/Value – Further implication for research and its marketing strategies in the field of clothing industry creating brand loyalty with customer.

Keywords: nudge, digital nudge, social proof, online buying, brand loyalty, trust, word of mouth

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Authors: Mohammad Mahmoud Mandurah

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The existence of InfoMiracles in scripture is evidence that the scripture has a divine origin. It is also evidence to the existence of God. An InfoMiracle is an information-based miracle. The basic component of an InfoMiracle is a piece of information that could not be obtained by a human except through a divine channel. The existence of a sufficient number of convincing InfoMiracles in a scripture necessitates the existence of the divine source to these InfoMiracles. A mathematical equation is developed to prove that the Qur’an has a divine origin, and hence, prove the existence of God. The equation depends on a single variable only, which is the number of InfoMiracles in the Qur’an. The Qur’an is rich with InfoMiracles. It is shown that the existence of less than 30 InfoMiracles in the Qur’an is sufficient proof to the existence of God and that the Qur’an is a revelation from God.

Keywords: InfoMiracle, God, mathematical proof, miracle, probability

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Authors: Mohamed A. Sullabi

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The importance of the formal specification in the software life cycle is barely concealing to anyone. Formal specifications use mathematical notation to describe the properties of information system precisely, without unduly constraining the way in how these properties are achieved. Having a correct and quality software specification is not easy task. This study concerns with how a group of rectifiers can communicate with each other and work to prepare and produce a correct formal software specification. WBCS has been implemented based mainly in the proposed supported cooperative work model and a survey conducted on the existing Webbased collaborative writing tools. This paper aims to assess the feasibility of executing the web-based collaboration process using WBCS. The purpose of conducting this test is to test the system as a whole for functionality and fitness for use based on the evaluation test plan.

Keywords: formal methods, formal specifications, collaborative writing, usability testing

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Authors: Zainab Magaji Musa, Nordin M. A. Rahman, Julaily Aida Jusoh

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The web services applications for digital reference service (WSDRS) of LIS model is an informal model that claims to reduce the problems of digital reference services in libraries. It uses web services technology to provide efficient way of satisfying users’ needs in the reference section of libraries. The formal WSDRS model consists of the Z specifications of all the informal specifications of the model. This paper discusses the formal validation of the Z specifications of WSDRS model. The authors formally verify and thus validate the properties of the model using Z/EVES theorem prover.

Keywords: validation, verification, formal, theorem prover

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Authors: Guowei Hou, Lixin Yu, Wei Zhuang, Hui Qin, Xue Yang

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Formal verification is proposed to ensure the correctness of the design and make functional verification more efficient. As cache plays a vital role in the design of System on Chip (SoC), and cache with Memory Management Unit (MMU) and cache memory unit makes the state space too large for simulation to verify, then a formal verification is presented for such system design. In the paper, a formal model checking verification flow is suggested and a new cache memory model which is called “exhaustive search model” is proposed. Instead of using large size ram to denote the whole cache memory, exhaustive search model employs just two cache blocks. For cache system contains data cache (Dcache) and instruction cache (Icache), Dcache memory model and Icache memory model are established separately using the same mechanism. At last, the novel model is employed to the verification of a cache which is module of a custom-built SoC system that has been applied in practical, and the result shows that the cache system is verified correctly using the exhaustive search model, and it makes the verification much more manageable and flexible.

Keywords: cache system, formal verification, novel model, system on chip (SoC)

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Authors: Jegede Oluseye Oladayo

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The study mapped innovation activities in the formal and informal mining sector in Nigeria. Data were collected through primary and secondary sources. Primary data were collected through guided questionnaire administration, guided interviews and personal observation. A purposive sampling method was adopted to select firms that are micro, small and medium enterprises. The study covered 100 (50 in the formal sector and 50 in the informal sector) purposively selected companies in south-western Nigeria. Secondary data were collected from different published sources. Data were analysed using descriptive and inferential statistics. Of the four types of technological innovations sampled, organisational innovation was found to be highest both in the formal (100%) and informal (100%) sectors, followed by process innovation: 60% in the formal sector and 28% in the informal sector, marketing innovation and diffusion based innovation were implemented by 64% and 4% respectively in the formal sector. There were no R&D activities (intramural or extramural) in both sectors, however, innovation activities occur at moderate levels in the formal sector. This is characterised by acquisition of machinery, equipment, hardware (100%), software (56), training (82%) and acquisition of external knowledge (60%) in the formal sector. In the informal sector, innovation activities were characterised by acquisition of external knowledge (100%), training/learning by experience (100%) and acquisition of tools (68%). The impact of innovation on firm’s performance in the formal sector was expressed mainly as increased capacity of production (100%), reduced production cost per unit of labour (88%), compliance with governmental regulatory requirements (72%) and entry on new markets (60%). In the informal sector, the impact of innovation was mainly expressed in improved flexibility of production (70%) and machinery/energy efficiency (70%). The important technological driver of process innovation in the mining sector was acquisition of machinery which accounts for the prevalence of 100% both in the formal and informal sectors. Next to this is training and re-training of technical staff, 74% in both the formal and the informal sector. Other factors influencing organisational innovation are skill of workforce with a prevalence of 80% in both the formal and informal sector. The important technological drivers include educational background of the manager/head of technical department (54%) for organisational innovation and (50%) for process innovation in the formal sector. The study concluded that innovation competence of the firms was mostly organisational changes.

Keywords: innovation prevalence, innovation activities, innovation performance, innovation drivers

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