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On the Average Complexity of Brzozowski's Algorithm for Deterministic Automata with a Small Number of Final States [chapter]

Sven De Felice, Cyril Nicaud
2014 Lecture Notes in Computer Science  
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

Sven De Felice, Cyril Nicaud
2016 International Journal of Foundations of Computer Science  
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]

Omar AitMous, Frédérique Bassino, Cyril Nicaud
2010 Lecture Notes in Computer Science  
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]

Shufang Zhu, Lucas M. Tabajara, Geguang Pu, Moshe Y. Vardi
2020 arXiv   pre-print
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]

Cyril Nicaud
2014 Lecture Notes in Computer Science  
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]

Sven De Felice, Cyril Nicaud
2013 Lecture Notes in Computer Science  
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

Julien David
2012 Theoretical Computer Science  
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

MARCO ALMEIDA, NELMA MOREIRA, ROGÉRIO REIS
2009 International Journal of Foundations of Computer Science  
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

Sabine Broda, António Machiavelo, Nelma Moreira, Rogério Reis
2015 Bulletin of the European Association for Theoretical Computer Science  
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

Hermann Gruber, Markus Holzer
2014 Electronic Proceedings in Theoretical Computer Science  
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

Hermann Gruber, Markus Holzer
2015 International Journal of Foundations of Computer Science  
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]

Vlad Slavici, Daniel Kunkle, Gene Cooperman, Stephen Linton
2011 arXiv   pre-print
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

Matthew Farrugia-Roberts, Bryn Jeffries, Harald Søndergaard
2022 Electronic Proceedings in Theoretical Computer Science  
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

Clemens Heuberger, Daniel Krenn, Sara Kropf
2016 Discrete Mathematics & Theoretical Computer Science  
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]

Clemens Heuberger, Daniel Krenn, Sara Kropf
2016 arXiv   pre-print
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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