All-Path Reachability Logic

Ștefănescu, Andrei; Ciobâcă, Ștefan; Mereuta, Radu; Moore, B.; Şerbănuţă, Traian Florin; Roşu, Grigore

doi:10.23638/lmcs-15(2:5)2019

Cited by 3 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we briefly recall LCTRSs [11], [24] and all-path reachability [7], [35], [36]. Familiarity with basic notions on abstract reduction systems and term rewriting [1], [30] is assumed.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

A Sufficient Condition of Logically Constrained Term Rewrite Systems for Decidability of All-path Reachability Problems with Constant Destinations

Kojima,

Nishida

2024

Journal of Information Processing

View full text Add to dashboard Cite

An all-path reachability (APR, for short) problem of a logically constrained term rewrite system (LCTRS, for short) is a pair of constrained terms representing state sets. An APR problem is demonically valid if every finite execution path from any state in the first set to an irreducible state includes a state in the second set. We have proposed a framework to reduce the non-occurrence of specified error states in a transition system represented by an LCTRS to an APR problem with irreducible constant destinations. In this paper, by focusing on quasi-termination of constrained narrowing, we characterize a class of LCTRSs of which APR problems with constant destinations are decidable. Quasi-termination of a (constrained) term w.r.t. narrowing is the finiteness of the set of reachable narrowed (constrained) terms from the initial (constrained) term up to variable renaming (and equivalence of constraints). To this end, we first introduce an inference rule for disproofs to a proof system for APR problems with constant destinations and formulate (dis)proof trees of APR problems in the style of cyclic proofs. Secondly, to prove correctness of disproof trees, we adapt constrained narrowing to LCTRSs and show soundness of constrained narrowing of LCTRSs w.r.t. constrained rewriting. Thirdly, we show a sufficient condition of LCTRSs for quasi-termination of constrained narrowing starting from linear constrained terms that have no nesting of defined symbols: Rewrite rules are right-linear and nesting-free w.r.t. defined symbols, and the application of rewrite rules for (mutually) recursive defined symbols does not increase the height of resulting constrained terms of narrowing. Finally, we show that if a constrained term is quasi-terminating w.r.t. narrowing of an LCTRS over a sort-wise finite signature with a decidable theory, then the APR problem consisting of the constrained term and an irreducible constant is decidable.

show abstract

Section: Preliminariesmentioning

confidence: 99%

“…[20], [21] is the application of APR problems. K framework [32] is a more general setting of rewriting than LCTRSs, and the proof system for all-path reachability has been implemented in K [35], [36]. A comparison of all-path reachability logic with CTL* can be seen in Ref.…”

Section: On Decidability Of Apr Problemsmentioning

confidence: 99%