Related papers: Structure-Aware Computing, Partial Quantifier Elim…
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…
Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…
Quantum computers have the potential of solving problems more efficiently than classical computers. While first commercial prototypes have become available, the performance of such machines in practical application is still subject to…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
This extended abstract accompanies an invited talk at CASC 2024, which surveys recent developments in Real Quantifier Elimination (QE) and Cylindrical Algebraic Decomposition (CAD). After introducing these concepts we will first consider…
Probabilistic membership filters are a type of data structure designed to quickly verify whether an element of a large data set belongs to a subset of the data. While false negatives are not possible, false positives are. Therefore, the…
We describe a method of model checking called Computing Range Reduction (CRR). The CRR method is based on derivation of clauses that reduce the set of traces of reachable states in such a way that at least one counterexample remains (if…
Conventional tools for formal hardware/software co-verification use bounded model checking techniques to construct a single monolithic propositional formula. Formulas generated in this way are extremely complex and contain a great deal of…
Quantifier elimination (QE) and Craig interpolation (CI) are central to various state-of-the-art automated approaches to hardware and software verification. They are rooted in the Boolean setting and are successful for, e.g., first-order…
Reasoning about quantum programs remains a fundamental challenge, regardless of the programming model or computational paradigm. Despite extensive research, existing verification techniques are insufficient -- even for quantum circuits, a…
Theorem provers has been used extensively in software engineering for software testing or verification. However, software is now so large and complex that additional architecture is needed to guide theorem provers as they try to generate…
We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. QE dates back to Tarski's work in the 1940s with software to perform it dating to the 1970s. There is a great body of work considering its…
Second-order quantifier elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
Software testing uses wide range of different tools to enhance the complicated process of defining quality of the system under test. Formal Concept Analysis (FCA) provides us with algorithms of deriving formal ontology from a set of objects…
Understanding the meaning of a text is a fundamental challenge of natural language understanding (NLU) and from its early days, it has received significant attention through question answering (QA) tasks. We introduce a general…
The paper presents our research on quantifier elimination (QE) for compositional reasoning and verification. For compositional reasoning, QE provides the foundation of our approach, serving as the calculus for composition to derive the…
Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal…
The current verification flow of complex systems uses different engines synergistically: virtual prototyping, formal verification, simulation, emulation and FPGA prototyping. However, none is able to verify a complete architecture.…
This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present in the given input formula $\phi^*$. The first enhancement…