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.

Tool support for learning Büchi automata and linear temporal logic

2008 ◽  
Vol 21 (3) ◽  
pp. 259-275 ◽  
Author(s):  
Yih-Kuen Tsay ◽  
Yu-Fang Chen ◽  
Ming-Hsien Tsai ◽  
Kang-Nien Wu ◽  
Wen-Chin Chan ◽  
...  
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Tool Support ◽  
Büchi Automata ◽  
Buchi Automata

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.

scholarly journals Synthesizing Good-Enough Strategies for LTLf Specifications

2021 ◽  
Author(s):  
Yong Li ◽  
Andrea Turrini ◽  
Moshe Y. Vardi ◽  
Lijun Zhang
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Synthesis Algorithm ◽  
Infinite Words ◽  
Büchi Automata ◽  
Winning Strategies ◽  
Deterministic Automata ◽  
Computationally Expensive ◽  
Buchi Automata

We consider the problem of synthesizing good-enough (GE)-strategies for linear temporal logic (LTL) over finite traces or LTLf for short. The problem of synthesizing GE-strategies for an LTL formula φ over infinite traces reduces to the problem of synthesizing winning strategies for the formula (∃Oφ)⇒φ where O is the set of propositions controlled by the system. We first prove that this reduction does not work for LTLf formulas. Then we show how to synthesize GE-strategies for LTLf formulas via the Good-Enough (GE)-synthesis of LTL formulas. Unfortunately, this requires to construct deterministic parity automata on infinite words, which is computationally expensive. We then show how to synthesize GE-strategies for LTLf formulas by a reduction to solving games played on deterministic Büchi automata, based on an easier construction of deterministic automata on finite words. We show empirically that our specialized synthesis algorithm for GE-strategies outperforms the algorithms going through GE-synthesis of LTL formulas by orders of magnitude.

scholarly journals UNITY and Büchi automata

2021 ◽  
Vol 33 (2) ◽  
pp. 185-205 ◽  
Author(s):  
Wim H. Hesselink
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Concurrent Program ◽  
Büchi Automata ◽  
Buchi Automata ◽  
Classical Construction

AbstractUNITY is a model for concurrent specifications with a complete logic for proving progress properties of the form “P leads to Q”. UNITY is generalized to U-specifications by giving more freedom to specify the steps that are to be taken infinitely often. In particular, these steps can correspond to non-total relations. The generalization keeps the logic sound and complete. The paper exploits the generalization in two ways. Firstly, the logic remains sound when the specification is extended with hypotheses of the form “F leads to G”. As the paper shows, this can make the logic incomplete. The generalization is used to show that the logic remains complete, if the added hypotheses “F leads to G” satisfy “F unless G”. The main result extends the applicability and completeness of UNITY logic to proofs that a given concurrent program satisfies any given formula of LTL, linear temporal logic, without the next-operator which is omitted because it is sensitive to stuttering. For this purpose, the program, written as a UNITY program, is extended with a number of boolean variables. The proof method relies on implementing the LTL formula, i.e., restricting the specification in such a way that only those runs remain that satisfy the formula. This result is a variation of the classical construction of a Büchi automatonfor a given LTL formula that accepts precisely those runs that satisfy the formula.

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.

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