Directed Reachability for Infinite-State Systems

Abstract

Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary time, which raises questions about the practical applicability of Petri nets as target models. In this paper, we introduce a novel approach for efficiently semi-deciding the reachability problem for Petri nets in practice. Our key insight is that computationally lightweight over-approximations of Petri nets can be used as distance oracles in classical graph exploration algorithms such as $$\mathsf {A}^{*}$$ A ∗ and greedy best-first search. We provide and evaluate a prototype implementation of our approach that outperforms existing state-of-the-art tools, sometimes by orders of magnitude, and which is also competitive with domain-specific tools on benchmarks coming from program synthesis and concurrent program analysis.

Property Directed Reachability for Generalized Petri Nets

“…It is difficult to find benchmarks with unbounded Petri nets. To quote Blondin et al [7], "due to the lack of tools handling reachability for unbounded state spaces, benchmarks arising in the literature are primarily coverability instances". It is also very difficult to randomly generate a true invariant that does not follow, in an obvious way, from the state equation.…”

“…For example, several algorithms are tailored for the discovery of counter-examples. We mention the tool FastForward [7] in our experiments, that explicitly targets the case of unbounded nets.…”

“…Reachability for Petri nets is an important and difficult problem with many practical applications: obviously for the formal verification of concurrent systems, but also for the study of diverse types of protocols (such as biological or business processes); the verification of software systems; the analysis of infinite state systems; etc. It is also a timely subject, as shown by recent publications on this subject [7,15], but also with the recent progress made on settling its theoretical complexity [12,13], which asserts that reachability is Ackermann-complete, and therefore inherently more complex than, say, the coverability problem. A practical consequence of this "inherent complexity", and a general consensus, is that we should not expect to find a one-size-fits-all algorithm that could be usable in practice.…”

“…The results obtained during the MCC highlight the very good performances achieved when putting all these techniques together, on bounded nets, with a collection of randomly generated properties. Another interesting feedback from the MCC is that simulation techniques are very good at finding a counter-example when a property is not an invariant [7,31].…”

Property Directed Reachability for Generalized Petri Nets

“…Reachability for Petri nets is an important and difficult problem with many practical applications: obviously for the formal verification of concurrent systems, but also for the study of diverse types of protocols (such as biological or business processes); the verification of software systems; the analysis of infinite state systems; etc. It is also a timely subject, as shown by recent publications on this subject [7,15], but also with the recent progress made on settling its theoretical complexity [12,13], which asserts that reachability is Ackermann-complete, and therefore inherently more complex than, say, the coverability problem.…”