Model checking with generalized Rabin and Fin-less automata

Abstract

In the automata theoretic approach to explicit state LTL model checking, the synchronized product of the model and an automaton that represents the negated formula is checked for emptiness. In practice, a (transition-based generalized) Büchi automaton (TGBA) is used for this procedure. This paper investigates whether using a more general form of acceptance, namely a transition-based generalized Rabin automaton (TGRA), improves the model checking procedure. TGRAs can have significantly fewer states than TGBAs; however, the corresponding emptiness checking procedure is more involved. With recent advances in probabilistic model checking and LTL to TGRA translators, it is only natural to ask whether checking a TGRA directly is more advantageous in practice. We designed a multi-core TGRA checking algorithm and performed experiments on a subset of the models and formulas from the 2015 Model Checking Contest and generated LTL formulas for models from the BEEM database. While we found little to no improvement by checking TGRAs directly, we show how various aspects of a TGRA's structure influences the model checking performance. In this paper, we also introduce a Finless acceptance condition, which is a disjunction of TGBAs. We show how to convert TGRAs into automata with Fin-less acceptance and show how a TGBA emptiness procedure can be extended to check Fin-less automata.

Determinization and Limit-determinization of Emerson-Lei automata

“…Translations from LTL to TELA have been proposed in [8,26,29], and all of them use product constructions to combine automata for subformulas. The emptiness-check for ω-automata under different types of acceptance conditions has been studied in [3,9,11,16], where [3] covers the general case of Emerson-Lei conditions and also considers qualitative probabilistic model checking using deterministic TELA. The generalized Rabin condition from [9,11] is equivalent to the special DNF that we use and a special case of the hyper-Rabin condition for which the emptiness problem is in P [1,10].…”

“…The emptiness-check for ω-automata under different types of acceptance conditions has been studied in [3,9,11,16], where [3] covers the general case of Emerson-Lei conditions and also considers qualitative probabilistic model checking using deterministic TELA. The generalized Rabin condition from [9,11] is equivalent to the special DNF that we use and a special case of the hyper-Rabin condition for which the emptiness problem is in P [1,10]. Probabilistic model checking for deterministic automata under this condition is considered in [11], while [9] is concerned with standard emptiness while allowing nondeterminism.…”

“…The generalized Rabin condition from [9,11] is equivalent to the special DNF that we use and a special case of the hyper-Rabin condition for which the emptiness problem is in P [1,10]. Probabilistic model checking for deterministic automata under this condition is considered in [11], while [9] is concerned with standard emptiness while allowing nondeterminism. A procedure to transform TELA into parity automata is presented in [33].…”

“…Using generalized acceptance conditions (e.g. generalized Büchi [13] or generalized Rabin [9,11]) and transition-based [18], rather than state-based, conditions are common techniques in this direction. An even more general approach has led to the HOA-format [2], which represents the acceptance condition as a positive Boolean formula over standard Büchi (Inf) and co-Büchi (Fin) conditions, also called Emerson-Lei conditions [1,34].…”

Introduction to Selected Papers from SPIN 2017

“…In "Model Checking with Generalized Rabin and Fin-less Automata" [1], authors Vincent Bloemen, Alexandre Duret-Lutz, and Jaco van de Pol explore the feasibility of using two alternative forms of automata with different acceptance conditions for model checking LTL properties. The new forms tend to generate fewer states, but have higher computational complexity.…”