Related papers: Satisfiability.jl: Satisfiability Modulo Theories …
We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool,…
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…
Generating proofs of unsatisfiability is a valuable capability of most SAT solvers, and is an active area of research for SMT solvers. This paper introduces the first method to efficiently generate proofs of unsatisfiability specifically…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with Both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short).…
Large Language Models (LLMs) have demonstrated formidable capabilities in solving mathematical problems, yet they may still commit logical reasoning and computational errors during the problem-solving process. Thus, this paper proposes a…
In this paper we present a satisfiability-preserving reduction from MITL interpreted over finitely-variable continuous behaviors to Constraint LTL over clocks, a variant of CLTL that is decidable, and for which an SMT-based bounded…
We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…
Answer Set Programming Modulo Theories (ASPMT) is an approach to combining answer set programming and satisfiability modulo theories based on the functional stable model semantics. It is shown that the tight fragment of ASPMT programs can…
We present a novel automata-based approach to address linear temporal logic modulo theory (LTL-MT) as a specification language for data words. LTL-MT extends LTL_f by replacing atomic propositions with quantifier-free multi-sorted…
Satisfiability solvers are increasingly playing a key role in software verification, with particularly effective use in the analysis of security vulnerabilities. String processing is a key part of many software applications, such as…
Logical reasoning about program data often requires dealing with heap structures as well as scalar data types. Recent advances in Satisfiability Modular Theory (SMT) already offer efficient procedures for dealing with scalars, yet they lack…
We present BSTModelKit.jl, an open-source Julia package for constructing, solving, and analyzing Biochemical Systems Theory (BST) models of biochemical networks. The package implements S-system representations, a canonical power-law…
Recent work has shown that Large Language Models (LLMs) are not only a suitable tool for code generation but also capable of generating annotation-based code specifications. Scaling these methodologies may allow us to deduce provable…
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…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…
Automated verification tools based on SMT solvers have made significant progress in verifying complex software systems. However, these tools face a fundamental tension between automation and performance when dealing with quantifier…
Microservice systems are becoming increasingly adopted due to their scalability, decentralized development, and support for continuous integration and delivery (CI/CD). However, this decentralized development by separate teams and…