Related papers: Equational Bit-Vector Solving via Strong Gr\"obner…
In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories…
This work focuses on effectively generating diverse solutions for satisfiability modulo theories (SMT) formulas, targeting the theories of bit-vectors, arrays, and uninterpreted functions, which is a critical task in software and hardware…
Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how solvers for satisfiability modulo theories (SMT…
While Large Language Models (LLMs) become ever more dominant, classic pre-trained word embeddings sustain their relevance through computational efficiency and nuanced linguistic interpretation. Drawing from recent studies demonstrating that…
A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…
We develop a Gr\"obner basis theory for a class of algebras that generalizes both PBW-algebras and rings of differential algebras on smooth varieties. Emphasis lies on methods to compute filtrations and graded structures defined by weight…
In [1] an integrable quantum model was introduced and a class of its cyclic representations was proven to define lattice regularizations of the Sine-Gordon model. Here, we analyze general cyclic representations of this integrable quantum…
We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
We study the strong convergence and bounded perturbation resilience of iterative algorithms based on the Generalized Modular String-Averaging (GMSA) procedure for infinite sequences of input operators under a general admissible control.…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
Propositional bounded model checking has been applied successfully to verify embedded software but is limited by the increasing propositional formula size and the loss of structure during the translation. These limitations can be reduced by…
Interest in anti-unification, the dual problem of unification, is on the rise due to applications within the field of software analysis and related areas. For example, anti-unification-based techniques have found uses within clone detection…
SMT solvers have been used successfully as reasoning engines for automated verification and other applications based on automated reasoning. Current techniques for dealing with quantified formulas in SMT are generally incomplete, forcing…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
Grover's algorithm can solve NP-complete problems on quantum computers faster than all the known algorithms on classical computers. However, Grover's algorithm still needs exponential time. Due to the BBBV theorem, Grover's algorithm is…
Satisfiability Modulo Counting (SMC) is a recently proposed general language to reason about problems integrating statistical and symbolic Artificial Intelligence. An SMC problem is an extended SAT problem in which the truth values of a few…
This short paper proposes to learn models of satisfiability modulo theories (SMT) formulas during solving. Specifically, we focus on infinite models for problems in the logic of linear arithmetic with uninterpreted functions (UFLIA). The…
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}_3$-invariant $R$-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…