Software model-checking as cyclic-proof search

Abstract

This paper shows that a variety of software model-checking algorithms can be seen as proof-search strategies for a non-standard proof system, known as a cyclic proof system . Our use of the cyclic proof system as a logical foundation of software model checking enables us to compare different algorithms, to reconstruct well-known algorithms from a few simple principles, and to obtain soundness proofs of algorithms for free. Among others, we show the significance of a heuristics based on a notion that we call maximal conservativity ; this explains the cores of important algorithms such as property-directed reachability (PDR) and reveals a surprising connection to an efficient solver of games over infinite graphs that was not regarded as a kind of PDR.

CycleQ: an efficient basis for cyclic equational reasoning

“…Since, in general, we cannot expect there to be any syntactical relationship between the node and its ancestor, the formation of cycles is closely related to the use of cuts in the proof. Indeed Tsukada and Unno [52] have demonstrated that many techniques developed for efficient software model checking can be viewed as the introduction of cuts into cyclic proofs to discharge proof obligations earlier.…”

“…Specifically, a cyclic proof system for separation logic has been given that automatically verifies that a program terminates [8,51]. Cyclic proof systems have recently been shown to subsume generic model-checking algorithms such as: lazy-abstraction with interpolants, property-directed reachability, and maximal conservativity for infinite game solving [52]. As with the generic cyclic theorem prover Cyclist, it is the choice of "matching-function" or "cut" that determines exactly how the verification algorithm operates outside of the usual reasoning on the abstract domain.…”

A study for recovering the cut-elimination property in cyclic proof systems by restricting the arity of inductive predicates

“…However, Saotome [14] suggested that there still exist sequents in the symbolic heap separation logic that cannot be found by a normal proof search procedure admitting (Cut) whose cut formulas are presumable from the goal sequent. Recently the framework of cyclic proof-search has been studied from the viewpoint of software verification [20,21].…”