Verification by approximate forward and backward reachability

Abstract

Approximate reachability techniques trade off accuracy for the capacity to deal with bigger desigw. In this paper, we extend the idea of approximations using overlapping projection to symbolic backward reachability. Thti is combined with a previous method of computing ouerapprom.mate forward reachable state sets using overlapping projections. The algom"thmcomputes a superset of the set of states that lie on a path from the initial state to a state that violates a specified invan.ant property. If this set h empty, there ti no possibility of violating the invan.ant. If this set is non-empty, it may be possible to prove the existence of such a path by searching for a counter-example. A simple heuristic is given, which seems to work well in practice, for generating a counter-example path from this appron.mation. JVe evaluate these new algom.thms by applying them to several control modules porn the I/O unit in the Stanford FLASH J!ultiprocessor.

A Roadmap for Formal Property Verification

“…These include cone-of-influence abstractions [38], counter-example guided abstraction refinement [40,63], and SAT-based abstraction refinement [42,107].…”

Counterexample-guided abstraction refinement for symbolic model checking

“…We believe that the methods described in these papers are orthogonal to our technique and may even be combined with our article in order to achieve better performance. A recent technique proposed by Govindaraju and Dill [1998] may be a starting point in this direction, since it also tries to identify the first spurious state in an abstract counterexample. It randomly chooses a concrete state corresponding to the first spurious state and tries to construct a real counterexample starting with the image of this state under the transition relation.…”

Mixing Forward and Backward Traversals in Guided-Prioritized BDD-Based Verification

“…We exploit approximate traversals [5] to simplify exact verification; we follow the guided search [6,7] paradigm when combining forward and backward [8,9] traversals to mutually focus and narrow their search area; we finally exploit conjunctive partitioning and cofactor based simplifications to keep BDD sizes under control. More specifically, we present what we call "inbound-path-search", i.e., a backward search approach based on partitioning and prioritized traversal.…”