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Symbolic Analysis by Using Folding Narrowing with Irreducibility and SMT Constraints

Published: 19 October 2023 Publication History

Abstract

Symbolic reachability analysis using rewriting with Satisfiability Modulo Theories (SMT) has been used to model different systems, including a variety of security protocols. Recently, it has also been used to analyze systems modeled using Parametric Timed Automata (PTAs). These techniques are based on reachability in a finite state graph generated from symbolic initial states where each generated state is constrained by an SMT expression checked for satisfiability. In this work, by rewriting with SMT but by narrowing with SMT. we use narrowing with SMT instead of rewriting with SMT. Narrowing with SMT allows a greater generalization, since (i) an infinite number of initial states may be represented by a finite number of states with variables, not only SMT variables, and (ii) an infinite state graph from an initial state may be represented by a finite state graph from another initial state with variables, not only SMT variables. We use graph search pruning techniques via irreducible terms and SMT constraints on conditional rules. This is supported by a novel folding SMT narrowing technique to represent infinite computations in a finite way. Additionally, we present a new textual user interface that allows the use of the algorithm in a simpler and more readable way.

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Cited By

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  • (2024)Maude2Lean: Theorem proving for Maude specifications using LeanJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2024.101005(101005)Online publication date: Aug-2024
  • (2024)Verifying Invariants by Deductive Model CheckingRewriting Logic and Its Applications10.1007/978-3-031-65941-6_1(3-21)Online publication date: 6-Apr-2024

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cover image ACM Conferences
FTSCS 2023: Proceedings of the 9th ACM SIGPLAN International Workshop on Formal Techniques for Safety-Critical Systems
October 2023
59 pages
ISBN:9798400703980
DOI:10.1145/3623503
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Published: 19 October 2023

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  1. Maude
  2. SMT constraints
  3. folding
  4. narrowing

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  • (2024)Maude2Lean: Theorem proving for Maude specifications using LeanJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2024.101005(101005)Online publication date: Aug-2024
  • (2024)Verifying Invariants by Deductive Model CheckingRewriting Logic and Its Applications10.1007/978-3-031-65941-6_1(3-21)Online publication date: 6-Apr-2024

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