scholarly journals From LTL to unambiguous Büchi automata via disambiguation of alternating automata

2021 ◽  
Author(s):  
Simon Jantsch ◽  
David Müller ◽  
Christel Baier ◽  
Joachim Klein
Keyword(s):  
Model Checking ◽  
Markov Chains ◽  
Important Application ◽  
High Complexity ◽  
The Core ◽  
Büchi Automata ◽  
Deterministic Automata ◽  
Tool Set ◽  
Buchi Automata ◽  
Alternating Automata

AbstractDue to the high complexity of translating linear temporal logic (LTL) to deterministic automata, several forms of “restricted” nondeterminism have been considered with the aim of maintaining some of the benefits of deterministic automata, while at the same time allowing more efficient translations from LTL. One of them is the notion of unambiguity. This paper proposes a new algorithm for the generation of unambiguous Büchi automata (UBA) from LTL formulas. Unlike other approaches it is based on a known translation from very weak alternating automata (VWAA) to NBA. A notion of unambiguity for alternating automata is introduced and it is shown that the VWAA-to-NBA translation preserves unambiguity. Checking unambiguity of VWAA is determined to be PSPACE-complete, both for the explicit and symbolic encodings of alternating automata. The core of the LTL-to-UBA translation is an iterative disambiguation procedure for VWAA. Several heuristics are introduced for different stages of the procedure. We report on an implementation of our approach in the tool and compare it to an existing LTL-to-UBA implementation in the tool set. Our experiments cover model checking of Markov chains, which is an important application of UBA.

Almost linear Büchi automata

2012 ◽  
Vol 22 (2) ◽  
pp. 203-235 ◽  
Author(s):  
TOMÁŠ BABIAK ◽  
VOJTĚCH ŘEHÁK ◽  
JAN STREJČEK
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Practical Relevance ◽  
New Class ◽  
Büchi Automata ◽  
Buchi Automata ◽  
Alternating Automata

We introduce a new fragment of linear temporal logic (LTL) called LIO and a new class of Büchi automata (BA) called almost linear Büchi automata (ALBA). We provide effective translations between LIO and ALBA showing that the two formalisms are expressively equivalent. As we expect there to be applications of our results in model checking, we use two standard sources of specification formulae, namely Spec Patterns and BEEM, to study the practical relevance of the LIO fragment, and to compare our translation of LIO to ALBA with two standard translations of LTL to BA using alternating automata. Finally, we demonstrate that the LIO to ALBA translation can be much faster than the standard translation, and the resulting automata can be substantially smaller.

scholarly journals Coinductive Algorithms for Büchi Automata

2021 ◽  
Vol 180 (4) ◽  
pp. 351-373
Author(s):  
Denis Kuperberg ◽  
Laureline Pinault ◽  
Damien Pous
Keyword(s):  
State Space ◽  
State Of The Art ◽  
The State ◽  
Specific Structure ◽  
Büchi Automata ◽  
Deterministic Automata ◽  
Buchi Automata ◽  
Language Equivalence ◽  
Art Techniques

We propose a new algorithm for checking language equivalence of non-deterministic Büchi automata. We start from a construction proposed by Calbrix, Nivat and Podelski, which makes it possible to reduce the problem to that of checking equivalence of automata on finite words. Although this construction generates large and highly non-deterministic automata, we show how to exploit their specific structure and apply state-of-the art techniques based on coinduction to reduce the state-space that has to be explored. Doing so, we obtain algorithms which do not require full determinisation or complementation.

Synthesis with Mandatory Stop Actions

2021 ◽  
Author(s):  
Giuseppe De Giacomo ◽  
Antonio Di Stasio ◽  
Giuseppe Perelli ◽  
Shufang Zhu
Keyword(s):  
Model Checking ◽  
Finite State Automata ◽  
Deep Impact ◽  
Synthesis Technique ◽  
Büchi Automata ◽  
Finite State ◽  
Ltl Synthesis ◽  
Buchi Automata ◽  
The Impact

We study the impact of the need for the agent to obligatorily instruct the action stop in her strategies. More specifically we consider synthesis (i.e., planning) for LTLf goals under LTL environment specifications in the case the agent must mandatorily stop at a certain point. We show that this obligation makes it impossible to exploit the liveness part of the LTL environment specifications to achieve her goal, effectively reducing the environment specifications to their safety part only. This has a deep impact on the efficiency of solving the synthesis, which can sidestep handling Buchi determinization associated to LTL synthesis, in favor of finite-state automata manipulation as in LTLf synthesis. Next, we add to the agent goal, expressed in LTLf, a safety goal, expressed in LTL. Safety goals must hold forever, even when the agent stops, since the environment can still continue its evolution. Hence the agent, before stopping, must ensure that her safety goal will be maintained even after she stops. To do synthesis in this case, we devise an effective approach that mixes a synthesis technique based on finite-state automata (as in the case of LTLf goals) and model-checking of nondeterministic Buchi automata. In this way, again, we sidestep Buchi automata determinization, hence getting a synthesis technique that is intrinsically simpler than standard LTL synthesis.

scholarly journals Certifying Inexpressibility

2021 ◽  
pp. 385-405
Author(s):  
Orna Kupferman ◽  
Salomon Sickert
Keyword(s):  
Winning Strategy ◽  
Expressive Power ◽  
The State ◽  
Infinite Words ◽  
Current State ◽  
Büchi Automata ◽  
Deterministic Automata ◽  
Buchi Automata

AbstractDifferent classes of automata on infinite words have different expressive power. Deciding whether a given language$$L \subseteq \varSigma ^\omega $$L⊆Σωcan be expressed by an automaton of a desired class can be reduced to deciding a game between Prover and Refuter: in each turn of the game, Refuter provides a letter in$$\varSigma $$Σ, and Prover responds with an annotation of the current state of the run (for example, in the case of Büchi automata, whether the state is accepting or rejecting, and in the case of parity automata, what the color of the state is). Prover wins if the sequence of annotations she generates is correct: it is an accepting run iff the word generated by Refuter is inL. We show how a winning strategy for Refuter can serve as a simple and easy-to-understand certificate to inexpressibility, and how it induces additional forms of certificates. Our framework handles all classes of deterministic automata, including ones with structural restrictions like weak automata. In addition, it can be used for refutingseparationof two languages by an automaton of the desired class, and for finding automata thatapproximateLand belong to the desired class.

Bounded Model Checking for Weak Alternating Büchi Automata

2006 ◽  
pp. 95-108 ◽  
Author(s):  
Keijo Heljanko ◽  
Tommi Junttila ◽  
Misa Keinänen ◽  
Martin Lange ◽  
Timo Latvala
Keyword(s):  
Model Checking ◽  
Bounded Model Checking ◽  
Büchi Automata ◽  
Buchi Automata
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