ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

On the Construction of Fine Automata for Safety Properties

Abstract: Of special interest in formal verification are safety properties, which assert that the system always stays within some allowed region. Each safety property ψ can be associated with a set of bad prefixes: a set of finite computations such that an infinite computation violates ψ iff it has a prefix in the set. By translating a safety property to an automaton for its set of bad prefixes, verification can be reduced to reasoning about finite words: a system is correct if none of its computations has a bad prefix. Checking the latter circumvents the need to reason about cycles and simplifies significantly methods like symbolic fixed-point based verification, bounded model checking, and more. A drawback of the translation lies in the size of the automata: while the translation of a safety LTL formula ψ to a nondeterministic Biichi automaton is exponential, its translation to a tight bad-prefix automaton - one that accepts all the bad prefixes of ψ, is doubly exponential. Kupferman and Vardi showed that for the purpose of verification, one can replace the tight automaton by a fine automaion - one that accepts at least one bad prefix of each infinite computation that violates ψ. They also showed that for many safety LTL formulas, a fine automaton has the same structure as the Buchi automaton for the formula. The problem of constructing fine automata for general safety LTL formulas was left open. In this paper we solve this problem and show that while a fine automaton cannot, in general, have the same structure as the Buchi automaton for the formula, the size of a fine automaton is still only exponential in the length of the formula.

Synchronizing words for weighted and timed automata

Abstract: The problem of synchronizing automata is concerned with the existence of a word that sends all states of the automaton to one and the same state. This problem has classically been studied for complete deterministic finite automata, with the existence problem being NLOGSPACE-complete. In this paper we consider synchronizing-word problems for weighted and timed automata. We consider the synchronization problem in several variants and combinations of these, including deterministic and non-deterministic timed and weighted automata, synchronization to unique location with possibly different clock valuations or accumulated weights, as well as synchronization with a safety condition forbidding the automaton to visit states outside a safety-set during synchronization (e.g. energy constraints). For deterministic weighted automata, the synchronization problem is proven PSPACE-complete under energy constraints, and in 3-EXPSPACE under general safety constraints. For timed automata the synchronization problems are shown to be PSPACE-complete in the deterministic case, and undecidable in the non-deterministic case.

Constructing NFAs by optimal use of positions in regular expressions

Abstract: We give two new algorithms for constructing small nondeterministic finite automata (NFA) from regular expressions. The first constructs NFAs with e-moves (eNFA) which are smaller than all the other eNFAs obtained by similar constructions. Their size is at most 3/2|α| + 5/2, where a is the regular expression. The second constructs NFAs. It uses e-elimination in the eNFAs we just introduced and builds a quotient of the well-known position automaton. Our NFA is always smaller and faster to compute than the position automaton. It uses optimally the information from the positions of a regular expression.

Sampling-based control synthesis for multi-robot systems under global temporal specifications

Abstract: This paper proposes a sampling-based algorithm for multi-robot control synthesis under global Linear Temporal Logic (LTL) formulas. Robot mobility is captured by transition systems whose states represent regions in the environment that satisfy atomic propositions. Existing planning approaches under global temporal goals rely on graph search techniques applied to a synchronous product automaton constructed among the robots. As the number of robots increases, the state-space of the product automaton grows exponentially and, as a result, graph search techniques become intractable. In this paper, we propose a new sampling-based algorithm that builds incrementally a directed tree that approximates the state-space and transitions of the synchronous product automaton. By approximating the product automaton by a tree rather than representing it explicitly, we require much fewer resources to store it and motion plans can be found by tracing the sequence of parent nodes from the leaves back to the root without the need for sophisticated graph search techniques. This significantly increases scalability of our algorithm compared to existing model-checking methods. We also show that our algorithm is probabilistically complete and asymptotically optimal and present numerical experiments that show that it can be used to model-check product automata with billions of states, which was not possible using an off-the-shelf model checker.