FORQ-Based Language Inclusion Formal Testing

Abstract

We propose a novel algorithm to decide the language inclusion between (nondeterministic) Büchi automata, a PSpace-complete problem. Our approach, like others before, leverage a notion of quasiorder to prune the search for a counterexample by discarding candidates which are subsumed by others for the quasiorder. Discarded candidates are guaranteed to not compromise the completeness of the algorithm. The novelty of our work lies in the quasiorder used to discard candidates. We introduce FORQs (family of right quasiorders) that we obtain by adapting the notion of family of right congruences put forward by Maler and Staiger in 1993. We define a FORQ-based inclusion algorithm which we prove correct and instantiate it for a specific FORQ, called the structural FORQ, induced by the Büchi automaton to the right of the inclusion sign. The resulting implementation, called Forklift, scales up better than the state-of-the-art on a variety of benchmarks including benchmarks from program verification and theorem proving for word combinatorics. Artifact:https://doi.org/10.5281/zenodo.6552870

AutoHyper: Explicit-State Model Checking for HyperLTL

“…Proposition 1 thus offers no asymptotic advantages over "standard" ABV in Section 3.1. In practice constructing an explicit complemented automaton is often unnecessary as the language inclusion or non-inclusion might be witnessed without a complete complementation [25,24,16,23]. This makes Proposition 1 relevant for the present work and the performance of AutoHyper.…”

“…AutoHyper uses spot [25] for LTL-to-NBA translations and automata complementations. To check language inclusion, AutoHyper uses spot (which is based on determinization), RABIT [16] (which is based on a Ramsey-based approach with heavy use of simulations), BAIT [24], and FORKLIFT [23] (both based on well-quasiorders). AutoHyper is designed such that communication with external automata tools is done via established text-based formats (opposed to proprietary APIs), namely the HANOI [1] and BA automaton formats.…”

“…Proposition 1). On the practical side, this enables AutoHyper to resort to a range of mature language inclusion checkers, including spot [25], RABIT [16], BAIT [24], and FORKLIFT [23].…”

From Spot 2.0 to Spot 2.10: What’s New?

“…Zielonka Trees and Alternating Cycle Decomposition [15,16] Spot this way), or to use it as a research/development toolbox, since it provides helper tools for generation of random formulas/automata, verification of LTLto-automata translation, simplifications, syntax conversions, etc. Nowadays, the algorithms for ω-automata implemented in Spot are often used as baseline for studying better algorithms [e.g., 18,25,32,33], but we also see some new applications built on top of ω-automata algorithms from Spot [e.g., 12,13].…”

Antichains Algorithms for the Inclusion Problem Between $$\omega $$-VPL

“…A key feature of such quasiorders is that the subset of L selected via the quasiorder must contain a counterexample to inclusion if there exists one. Quasiorders are a versatile heuristic that has been applied to inclusion problems for languages such as languages of finite words [3,10,14] (including visibly pushdown language [6]) or infinite words [1,2,12,13,16,24] and even tree languages [3,5]. Algorithms leveraging quasiorders are commonly referred to as antichains algorithms.…”