Related papers: Structure-Aware Computing, Partial Quantifier Elim…
We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage…
Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article,…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
This paper proposes SAT-based techniques to calculate a specific normal form of a given finite mathematical structure (model). The normal form is obtained by permuting the domain elements so that the representation of the structure is…
Formal verification of neural networks is an active topic of research, and recent advances have significantly increased the size of the networks that verification tools can handle. However, most methods are designed for verification of an…
Most formal methods see the correctness of a software system as a binary decision. However, proving the correctness of complex systems completely is difficult because they are composed of multiple components, usage scenarios, and…
Quantum computing (QC) represents the future of computing systems, but the tools for reasoning about the quantum model of computation, in which the laws obeyed are those on the quantum mechanical scale, are still a mix of linear algebra and…
Segment Anything Model (SAM) exhibits remarkable zero-shot segmentation capability; however, its prohibitive computational costs make edge deployment challenging. Although post-training quantization (PTQ) offers a promising compression…
Cluster analysis plays a very important role in data analysis. In these years, cluster ensemble, as a cluster analysis tool, has drawn much attention for its robustness, stability, and accuracy. Many efforts have been done to combine…
This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…
Approximate Membership Query structures (AMQs) rely on randomisation for time- and space-efficiency, while introducing a possibility of false positive and false negative answers. Correctness proofs of such structures involve subtle…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…
There have been several efforts to apply quantum SAT solving methods to factor large integers. While these methods may provide insight into quantum SAT solving, to date they have not led to a convincing path to integer factorization that is…
We consider problems originating in economics that may be solved automatically using mathematical software. We present and make freely available a new benchmark set of such problems. The problems have been shown to fall within the framework…
Generalized quantifiers (e.g., few, most) are used to indicate the proportions predicates are satisfied (for example, some apples are red). One way to interpret quantifier semantics is to explicitly bind these satisfactions with percentage…
Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly reduces the complexity of computation. Then, the stability…
In this paper, we conduct a systematic literature review of (semi-) automated approaches to Quantum Software Engineering (QSE) and Quantum Artificial Intelligence (QAI). Prior work in the literature indicated that both Software Engineering…
With the range and sensitivity of algorithmic decisions expanding at a break-neck speed, it is imperative that we aggressively investigate whether programs are biased. We propose a novel probabilistic program analysis technique and apply it…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…