A Package TESTAS for Checking Some Kinds of Testability

Trahtman, A. N.

doi:10.1007/3-540-44977-9_22

Cited by 9 publications

(13 citation statements)

References 28 publications

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“…The average computation time is about 100 up to 1000 times faster than the time of Trahtman's program TESTAS (Trahtman 2003(Trahtman , 2006 for binary automata with 50 states. The reduction to SAT used in (Skvortsov and Tipikin 2011) seemed to be the fastest recently known algorithm and the reported average time for 50 states automata is 2.7 seconds, and for 100 states automata is 70 seconds.…”

Section: Efficiencymentioning

confidence: 97%

“…Most naturally, the breadth-first-search (BFS) method is used which starts from the set of all states of the given automaton and forms images applying letter transformations until a singleton is reached. Based on these ideas computation packages have been created [TESTAS (Trahtman 2003) and recently developed COMPAS (Chmiel and Roman 2011)]. In (Roman 2009a), Roman uses a genetic algorithm to find a reset word of randomly generated automata and thus obtains upper bounds on the reset length.…”

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confidence: 99%

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Computing the shortest reset words of synchronizing automata

2013

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In this paper we give the details of our new algorithm for finding minimal reset words of finite synchronizing automata. The problem is known to be computationally hard, so our algorithm is exponential in the worst case, but it is faster than the algorithms used so far and it performs well on average. The main idea is to use a bidirectional breadth-first-search and radix (Patricia) tries to store and compare subsets. A good performance is due to a number of heuristics we apply and describe here in a suitable detail. We give both theoretical and practical arguments showing that the effective branching factor is considerably reduced. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with up to n = 350 states and up to k = 10 input letters. In particular, we obtain a new estimation of the expected length of the shortest reset word ≈ 2.5 √ n − 5 for binary automata and show that the error of this estimate is sufficiently small. Experiments for automata with more than two input letters show certain trends with the same general pattern.

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Section: Efficiencymentioning

confidence: 97%

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confidence: 99%

Computing the shortest reset words of synchronizing automata

2013

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“…Mappings with the same set of states are identified. It essentially simplified the process in comparison with the algorithm from [17]. Distinct mappings are saved.…”

Section: An Algorithm For Finding Synchronizing Word Of Minimal Lengthmentioning

confidence: 99%

An Efficient Algorithm Finds Noticeable Trends and Examples Concerning the Černy Conjecture

Trahtman

2006

Lecture Notes in Computer Science

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Abstract. A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. JanČerny had found in 1964 a sequence of n-state complete DFA with shortest synchronizing word of length (n − 1) 2 . He had conjectured that it is an upper bound for the length of the shortest synchronizing word for any n-state complete DFA. The examples of DFA with shortest synchronizing word of length (n−1) 2 are relatively rare. To theČerny sequence were added in all examples of Cerny, Piricka and Rosenauerova (1971), of Kari (2001) and of Roman (2004). By help of a program based on some effective algorithms, a wide class of automata of size less than 11 was checked. The order of the algorithm finding synchronizing word is quadratic for overwhelming majority of known to date automata. Some new examples of n-state DFA with minimal synchronizing word of length (n − 1) 2 were discovered. The program recognized some remarkable trends concerning the length of the minimal synchronizing word.

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“…The average computation time is about 100 or 1000 times faster than the time of Trahtman's program TESTAS [22,23] for automata with 50 states. The reduction to SAT used in [20] seemed to be the fastest recently known algorithm and the reported average time for 50 states automata is 2.7 seconds, and for 100 states automata is 70 seconds.…”

Section: Computationsmentioning

confidence: 96%

A Fast Algorithm Finding the Shortest Reset Words

Kisielewicz

Kowalski

Szykuła

2013

Lecture Notes in Computer Science

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In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far and it works well in practice. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare resulted subsets. We give both theoretical and practical arguments showing that the branching factor is reduced efficiently. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with $n$ states and 2 input letters. We follow Skvorsov and Tipikin, who have performed such a study using a SAT solver and considering automata up to $n=100$ states. With our algorithm we are able to consider much larger sample of automata with up to $n=300$ states. In particular, we obtain a new more precise estimation of the expected length of the shortest reset word $\approx 2.5\sqrt{n-5}$.Comment: COCOON 2013. The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1

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A Package TESTAS for Checking Some Kinds of Testability

Cited by 9 publications

References 28 publications

Computing the shortest reset words of synchronizing automata

Computing the shortest reset words of synchronizing automata

An Efficient Algorithm Finds Noticeable Trends and Examples Concerning the Černy Conjecture

A Fast Algorithm Finding the Shortest Reset Words

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