Automatically Proving and Disproving Feasibility Conditions

Abstract

In the realm of term rewriting, given terms s and t, a reachability condition s → * t is called feasible if there is a substitution σ such that σ(s) rewrites into σ(t) in zero or more steps; otherwise, it is called infeasible. Checking infeasibility of (sequences of) reachability conditions is important in the analysis of computational properties of rewrite systems like confluence or (operational) termination. In this paper, we generalize this notion of feasibility to arbitrary n-ary relations on terms defined by first-order theories. In this way, properties of computational systems whose operational semantics can be given as a first-order theory can be investigated. We introduce a framework for proving feasibility/infeasibility, and a new tool, infChecker, which implements it.

Term Orderings for Non-reachability of (Conditional) Rewriting

“…The only implemented way of combining their power is a naive one: apply the tests one by one while they fail. For future work, it will be interesting to incorporate the proposed method into the existing frameworks [10,30].…”

“…Definition 6 (π-simplicity). We say a related Under these conditions, it is known that WPO is closed under contexts and WPO is compatible with WPO [36, Lemmas 7,10,13]. Later in this section we prove other properties necessary for Proposition 1, for which the claims in [36] must be generalized for the purpose of this paper.…”

“…Sternagel and Yamada [30] proposed a framework for analyzing reachability by combining basic logical manipulations, and Gutiérrez and Lucas [10] proposed another framework, similar to the dependency pair framework. The present work focuses on atomic analysis techniques, and is orthogonal to these efforts of combining techniques.…”

mu-term: Verify Termination Properties Automatically (System Description)

“…. , s n n t n (called f-sequences [15]) where s i and t i are terms and i are predicates → * i that capture the possibility of having two nodes involved in a chain [20, Sect. 4.5] and must be proved feasible or infeasible (for some substitution σ which applies to terms s i and t i ).…”

Applications and extensions of context-sensitive rewriting

“…13 If ( 5) is feasible, then a ground term t exists that satisfies (iii). The tool infChecker 14 [59] is able to deal with such kind of (in)feasibility problems involving CSR.…”