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On the Average Complexity of Brzozowski's Algorithm for Deterministic Automata with a Small Number of Final States
[chapter]
2014
Lecture Notes in Computer Science
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We analyze the average complexity of Brzozowski's minimization algorithm for distributions of deterministic automata with a small number of final states. ...
We show that, as in the case of the uniform distribution, the average complexity is super-polynomial even if we consider random deterministic automata with only one final state. ...
We would like to thanks Jean-François Marckert for his patient explanation of his result on the width of random Cayley trees [?]. ...
doi:10.1007/978-3-319-09698-8_3
fatcat:goq27q4o7fbozcy3pupogmm5ey
Average Case Analysis of Brzozowski's Algorithm
2016
International Journal of Foundations of Computer Science
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a small number of final states. ...
Received (Day Month Year) Accepted (Day Month Year) Communicated by (xxxxxxxxxx) We analyze the average complexity of Brzozowski's minimization algorithm for distributions of deterministic automata with ...
We would like to thanks Jean-François Marckert for his crystal clear explanation of his result on the width of random Cayley trees [5] . ...
doi:10.1142/s0129054116400025
fatcat:c6axjsmj5fgrpeewkmyqxryw7q
Building the Minimal Automaton of A * X in Linear Time, When X Is of Bounded Cardinality
[chapter]
2010
Lecture Notes in Computer Science
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This algorithm, inspired by Brzozowski's minimization algorithm, uses sparse lists to achieve a linear time complexity with respect to n. ...
We present an algorithm for constructing the minimal automaton recognizing A * X, where the pattern X is a set of m (that is a fixed integer) non-empty words over a finite alphabet A whose sum of lengths ...
For more details, the reader is referred to [9] for automata and to [6, 7] for algorithms on strings. Automata. ...
doi:10.1007/978-3-642-13509-5_25
fatcat:3ubx2ufikfehvdncaabmftqdrm
On the Power of Automata Minimization in Temporal Synthesis
[article]
2020
arXiv
pre-print
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Analyzing the results, we observe that the reason for the poor performance of Brzozowski's algorithm is a discrepancy between theory and practice. ...
Reactive synthesis is the problem of automatically constructing a reactive system from a formal specification, with the guarantee that the executions of the system align with the specification. ...
We present two approaches for performing the final determinization step in Brzozowski's algorithm: one explicit using routines implemented in the SPOT automata library [16] , and one symbolic which converts ...
arXiv:2008.06790v1
fatcat:eub57am5fvhrhnwl5mdwanq7wu
Random Deterministic Automata
[chapter]
2014
Lecture Notes in Computer Science
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In this article, we consider deterministic automata under the paradigm of average case analysis of algorithms. ...
, such as the average running time of Moore's state minimization algorithm or the estimation of the probability that an automaton is minimal. ...
The author would like to thank Arnaud Carayol for his precious help during the preparation of this article. ...
doi:10.1007/978-3-662-44522-8_2
fatcat:5uqwdjrplbbl5fngl5ga2xs4ii
Brzozowski Algorithm Is Generically Super-Polynomial for Deterministic Automata
[chapter]
2013
Lecture Notes in Computer Science
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As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for the uniform distribution on deterministic automata. ...
We study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. ...
We would like to thanks Andrea Sportiello for the fruitful technical discussion we had in Cluny, which, amongst many other things, lead to the proof of Proposition 1. ...
doi:10.1007/978-3-642-38771-5_17
fatcat:gui4x4yc5ral7bh4vxgkaekb74
Average complexity of Moore's and Hopcroft's algorithms
2012
Theoretical Computer Science
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In this paper we prove that for the uniform distribution on complete deterministic automata, the average time complexity of Moore's state minimization algorithm is O(n log log n), where n is the number ...
of states in the input automata and the number of letters in the alphabet is fixed. ...
Finally, Brzozowski's algorithm [9, 13, 12] is different from the other ones. Its inputs may be non-deterministic automata. ...
doi:10.1016/j.tcs.2011.10.011
fatcat:3ugzhycbufcfrmllzsdjtytuui
ANTIMIROV AND MOSSES'S REWRITE SYSTEM REVISITED
2009
International Journal of Foundations of Computer Science
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Antimirov and Mosses proposed a rewrite system for deciding the equivalence of two (extended) regular expressions. ...
Besides an improved version of Antimirov and Mosses's algorithm, we present a version using partial derivatives. ...
The worst case complexity of the automata determinization process is exponential in the number of states. ...
doi:10.1142/s0129054109006802
fatcat:pe473d5krvdebeye5ickxztfn4
Average Size of Automata Constructions from Regular Expressions
2015
Bulletin of the European Association for Theoretical Computer Science
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The worst case of both the complexity of the conversion algorithms, and of the size of the resulting automata, are well studied. ...
In this paper we review recent results on the average size of automata resulting from several constructions and suggest several directions of research. ...
Thus, the average number of its states coincides with the average number of letters determined in Equation (10) , i.e. asymptotically and on average the number of states of A pos (α) is half the size ...
dblp:journals/eatcs/BrodaMMR15
fatcat:joz6ogapdnfb5bwkxommtfy4my
From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity
2014
Electronic Proceedings in Theoretical Computer Science
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Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination ...
In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. ...
Thanks to Sebastian Jakobi for helpful comments and suggestions on an earlier draft of this paper. ...
doi:10.4204/eptcs.151.2
fatcat:xiiyglxcebbkpdklmkngqd47dm
From Finite Automata to Regular Expressions and Back — A Summary on Descriptional Complexity
2015
International Journal of Foundations of Computer Science
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Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination ...
In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. ...
Thanks to Sebastian Jakobi for helpful comments and suggestions on an earlier draft of this paper. ...
doi:10.1142/s0129054115400110
fatcat:glifsfoc4jgw7cpuyxjwlwcq6a
Finding the Minimal DFA of Very Large Finite State Automata with an Application to Token Passing Networks
[article]
2011
arXiv
pre-print
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Two of the most important algorithms for FSA processing are the conversion of a non-deterministic finite automaton (NFA) to a deterministic finite automaton (DFA), and then the production of the unique ...
That computation produced an intermediate DFA with 525,000 states and an unreported number of states for the corresponding minimal DFA. ...
The average subset size (the sum of all subset sizes divided by the number of subsets) increases slightly with stack depth, from an average of 8.48 states per set for stack depth 8 to 10.06 states per ...
arXiv:1103.5736v1
fatcat:zrx7suswn5fjljwh3kvjdhxpiy
Teaching Simple Constructive Proofs with Haskell Programs
2022
Electronic Proceedings in Theoretical Computer Science
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2022 pre-print arXiv:2208.04699v1 fatcat:ssmmnd3x2zhtrpdlv2enpjvcmq
One of the hardest exercises to convert into this format are traditional written proofs conveying constructive arguments. In this paper we reflect on the digitisation of this kind of exercise. ...
This discussion contributes to our broader exploration of programming problems as a flexible digital medium for learning and assessment. ...
Acknowledgements We thank our teaching colleagues Anna Kalenkova, Bach Le, Billy Price, Rohan Hitchcock, and the rest of the COMP30026 teaching team. ...
doi:10.4204/eptcs.363.4
fatcat:wgopatz5nfh6rkplo67hnshjba
Automata in SageMath---Combinatorics meet Theoretical Computer Science
2016
Discrete Mathematics & Theoretical Computer Science
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In particular, we compute the asymptotic Hamming weight of a non-adjacent-form-like digit expansion, which was not known before. ...
The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. ...
For instance, SageMath's package implements Moore's algorithm for minimization of deterministic automata, . Additionally, the user may also choose Brzozowski's algorithm. ...
doi:10.46298/dmtcs.1352
fatcat:n7e6ed3bmbhqdg2ydouozvgilm
Automata in SageMath---Combinatorics meet Theoretical Computer Science
[article]
2016
arXiv
pre-print
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In particular, we compute the asymptotic Hamming weight of a non-adjacent-form-like digit expansion, which was not known before. ...
The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. ...
For instance, SageMath's package implements Moore's algorithm for minimization of deterministic automata, . Additionally, the user may also choose Brzozowski's algorithm. ...
arXiv:1404.7458v4
fatcat:prnbvuqeu5fpdphdhrajffbzta
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