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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
*

We analyze

doi:10.1007/978-3-319-09698-8_3
fatcat:goq27q4o7fbozcy3pupogmm5ey
*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 [?]. ...##
###
Average Case Analysis of Brzozowski's Algorithm

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] . ...

##
###
Building the Minimal Automaton of A * X in Linear Time, When X Is of Bounded Cardinality
[chapter]

2010
*
Lecture Notes in Computer Science
*

This

doi:10.1007/978-3-642-13509-5_25
fatcat:3ubx2ufikfehvdncaabmftqdrm
*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*. ...##
###
On the Power of Automata Minimization in Temporal Synthesis
[article]

2020
*
arXiv
*
pre-print

Analyzing

arXiv:2008.06790v1
fatcat:eub57am5fvhrhnwl5mdwanq7wu
*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 ...##
###
Random Deterministic Automata
[chapter]

2014
*
Lecture Notes in Computer Science
*

In this article, we consider

doi:10.1007/978-3-662-44522-8_2
fatcat:5uqwdjrplbbl5fngl5ga2xs4ii
*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. ...##
###
Brzozowski Algorithm Is Generically Super-Polynomial for Deterministic Automata
[chapter]

2013
*
Lecture Notes in Computer Science
*

As

doi:10.1007/978-3-642-38771-5_17
fatcat:gui4x4yc5ral7bh4vxgkaekb74
*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. ...##
###
Average complexity of Moore's and Hopcroft's algorithms

2012
*
Theoretical Computer Science
*

In this paper we prove that

doi:10.1016/j.tcs.2011.10.011
fatcat:3ugzhycbufcfrmllzsdjtytuui
*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*. ...##
###
ANTIMIROV AND MOSSES'S REWRITE SYSTEM REVISITED

2009
*
International Journal of Foundations of Computer Science
*

Antimirov and Mosses proposed

doi:10.1142/s0129054109006802
fatcat:pe473d5krvdebeye5ickxztfn4
*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*. ...##
###
Average Size of Automata Constructions from Regular Expressions

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 ...

##
###
From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity

2014
*
Electronic Proceedings in Theoretical Computer Science
*

Moreover, we report

doi:10.4204/eptcs.151.2
fatcat:xiiyglxcebbkpdklmkngqd47dm
*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. ...##
###
From Finite Automata to Regular Expressions and Back — A Summary on Descriptional Complexity

2015
*
International Journal of Foundations of Computer Science
*

Moreover, we report

doi:10.1142/s0129054115400110
fatcat:glifsfoc4jgw7cpuyxjwlwcq6a
*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. ...##
###
Finding the Minimal DFA of Very Large Finite State Automata with an Application to Token Passing Networks
[article]

2011
*
arXiv
*
pre-print

Two

arXiv:1103.5736v1
fatcat:zrx7suswn5fjljwh3kvjdhxpiy
*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 ...##
###
Teaching Simple Constructive Proofs with Haskell Programs

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. ...

##
###
Automata in SageMath---Combinatorics meet Theoretical Computer Science

2016
*
Discrete Mathematics & Theoretical Computer Science
*

In particular, we compute

doi:10.46298/dmtcs.1352
fatcat:n7e6ed3bmbhqdg2ydouozvgilm
*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*. ...##
###
Automata in SageMath---Combinatorics meet Theoretical Computer Science
[article]

2016
*
arXiv
*
pre-print

In particular, we compute

arXiv:1404.7458v4
fatcat:prnbvuqeu5fpdphdhrajffbzta
*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*. ...
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