Learning to Prove Safety over Parameterised Concurrent Systems (Full Version)

We revisit the classic problem of proving safety over parameterised concurrent systems, i.e., an infinite family of finite-state concurrent systems that are represented by some finite (symbolic) means. An example of such an infinite family is a dining philosopher protocol with any number n of processes (n being the parameter that defines the infinite family). Regular model checking is a well-known generic framework for modelling parameterised concurrent systems, where an infinite set of configurations (resp. transitions) is represented by a regular set (resp. regular transducer). Although verifying safety properties in the regular model checking framework is undecidable in general, many sophisticated semi-algorithms have been developed in the past fifteen years that can successfully prove safety in many practical instances. In this paper, we propose a simple solution to synthesise regular inductive invariants that makes use of Angluin's classic L* algorithm (and its variants). We provide a termination guarantee when the set of configurations reachable from a given set of initial configurations is regular. We have tested L* algorithm on standard (as well as new) examples in regular model checking including the dining philosopher protocol, the dining cryptographer protocol, and several mutual exclusion protocols (e.g. Bakery, Burns, Szymanski, and German). Our experiments show that, despite the simplicity of our solution, it can perform at least as well as existing semi-algorithms.Comment: Full version of FMCAD'17 pape

Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

This paper investigates the verification and synthesis of parameterized protocols that satisfy leadsto properties $R \leadsto Q$ on symmetric unidirectional rings (a.k.a. uni-rings) of deterministic and constant-space processes under no fairness and interleaving semantics, where $R$ and $Q$ are global state predicates. First, we show that verifying $R \leadsto Q$ for parameterized protocols on symmetric uni-rings is undecidable, even for deterministic and constant-space processes, and conjunctive state predicates. Then, we show that surprisingly synthesizing symmetric uni-ring protocols that satisfy $R \leadsto Q$ is actually decidable. We identify necessary and sufficient conditions for the decidability of synthesis based on which we devise a sound and complete polynomial-time algorithm that takes the predicates $R$ and $Q$, and automatically generates a parameterized protocol that satisfies $R \leadsto Q$ for unbounded (but finite) ring sizes. Moreover, we present some decidability results for cases where leadsto is required from multiple distinct $R$ predicates to different $Q$ predicates. To demonstrate the practicality of our synthesis method, we synthesize some parameterized protocols, including agreement and parity protocols

Learning Interpretable Temporal Properties from Positive Examples Only

We consider the problem of explaining the temporal behavior of black-boxsystems using human-interpretable models. To this end, based on recent researchtrends, we rely on the fundamental yet interpretable models of deterministicfinite automata (DFAs) and linear temporal logic (LTL) formulas. In contrast tomost existing works for learning DFAs and LTL formulas, we rely on onlypositive examples. Our motivation is that negative examples are generallydifficult to observe, in particular, from black-box systems. To learnmeaningful models from positive examples only, we design algorithms that relyon conciseness and language minimality of models as regularizers. To this end,our algorithms adopt two approaches: a symbolic and a counterexample-guidedone. While the symbolic approach exploits an efficient encoding of languageminimality as a constraint satisfaction problem, the counterexample-guided onerelies on generating suitable negative examples to prune the search. Both theapproaches provide us with effective algorithms with theoretical guarantees onthe learned models. To assess the effectiveness of our algorithms, we evaluateall of them on synthetic data.<br

Inferring network invariants automatically

Abstract. Verification by network invariants is a heuristic to solve uniform verification of parameterized systems. Given a system P, a network invariant for P is a system that abstracts the composition of every number of copies of P running in parallel. If there is such a network invariant, by reasoning about it, uniform verification with respect to the family P [1] ‖ · · · ‖ P [n] can be carried out. In this paper, we propose a procedure that searches systematically for a network invariant satisfying a given safety property. The search is based on algorithms for learning finite automata due to Angluin and Biermann. We optimize the search by combining both algorithms for improving successive possible invariants. We also show how to reduce the learning problem to SAT, allowing efficient SAT solvers to be used, which turns out to yield a very competitive learning algorithm. The overall search procedure finds a minimal such invariant, if it exists.

Inferring network invariants automatically

Abstract. Verification by network invariants is a heuristic to solve uniform verification of parameterized systems. Given a system P, a network invariant for P is a system that abstracts the composition of every number of copies of P running in parallel. If there is such a network invariant, by reasoning about it, uniform verification with respect to the family P [1] � · · · � P [n] can be carried out. In this paper, we propose a procedure that searches systematically for a network invariant satisfying a given safety property. The search is based on algorithms for learning finite automata due to Angluin and Biermann. We optimize the search by combining both algorithms for improving successive possible invariants. We also show how to reduce the learning problem to SAT, allowing efficient SAT solvers to be used, which turns out to yield a very competitive learning algorithm. The overall search procedure finds a minimal such invariant, if it exists.