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One of the fundamental results in quantum foundations is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as…
In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of…
Due to the increasing volume, volatility, and diversity of data in virtually all areas of our lives, the ability to detect duplicates in potentially linked data sources is more important than ever before. However, while research is already…
In this article, we show that the completion problem, i.e. the decision problem whether a partial structure can be completed to a full structure, is NP-complete for many combinatorial structures. While the gadgets for most reductions in…
Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…
Some test amplification tools extend a manually created test suite with additional test cases to increase the code coverage. The technique is effective, in the sense that it suggests strong and understandable test cases, generally adopted…
The need for reducing manufacturing defect escape in today's safety-critical applications requires increased fault coverage. However, generating a test set using commercial automatic test pattern generation (ATPG) tools that lead to…
As datasets continue to grow, neural network (NN) applications are becoming increasingly limited by both the amount of available computational power and the ease of developing high-performance applications. Researchers often must have…
A simple yet successful approach to parallel satisfiability (SAT) solving is to run several different (a portfolio of) SAT solvers on the input problem at the same time until one solver finds a solution. The SAT solvers in the portfolio can…
A major challenge in testing software product lines is efficiency. In particular, testing a product line should take less effort than testing each and every product individually. We address this issue in the context of input-output…
Web applications are distributed applications, they are programs that run on more than one computer and communicate through a network or server. This very distributed nature of web applications, combined with the scale and sheer complexity…
This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…
Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…
An (encoded) decision problem is a pair (E, F) where E=words that encode instances of the problem, F=words to be accepted. We use "strings" in a technical sense. With an NP problem (E, F) we associate the "logogram" of F relative to E,…
The IC3 algorithm, also known as PDR, is a SAT-based model checking algorithm that has significantly influenced the field in recent years due to its efficiency, scalability, and completeness. It utilizes SAT solvers to solve a series of SAT…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
The use of Boolean Satisfiability (SAT) solver for hardware verification incurs exponential run-time in several instances. In this work we have proposed an efficient quantum SAT (qSAT) solver for equivalence checking of Boolean circuits…
In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical…