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Minimisation of Deterministic Parity and Buchi Automata and Relative Minimisation of Deterministic Finite Automata [article]

Sven Schewe
2011 arXiv   pre-print
In this report we study the problem of minimising deterministic automata over finite and infinite words.  ...  put on top of it.  ...  of finite automata, and the minimisation of Büchi and Co-Büchi automata.  ... 
arXiv:1007.1333v2 fatcat:bv64datkofffzgeiilypyi6n3u

Beyond Hyper-Minimisation---Minimising DBAs and DPAs is NP-Complete

Sven Schewe, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
In this paper we study the problem of minimising deterministic automata over finite and infinite words.  ...  relations on automata become coarser from left to right.  ...  We also read finite automata at times as Büchi (or Co-Büchi) automata and Büchi (or Co-Büchi) automata as finite automata in the constructions, and let DFAs run on infinite words where this is convenient  ... 
doi:10.4230/lipics.fsttcs.2010.400 dblp:conf/fsttcs/Schewe10 fatcat:m76buen6ljcwbmnykl7ltwz26u

Minimizing local automata

Marie-Pierre Beal, Maxime Crochemore
2007 2007 IEEE International Symposium on Information Theory  
These automata, also called covers, recognize symbolic dynamical shifts of finite type.  ...  While Hopcroft's algorithm relies on a "negative strategy", starting from a partition with a single class of all states, and partitioning classes when it is discovered that two states cannot belong to  ...  MINIMISATION OF DETERMINISTIC AFT AUTOMATA A. Minimisation by a sequence of state mergings Let A = (Q, E) be a deterministic automaton.  ... 
doi:10.1109/isit.2007.4557131 dblp:conf/isit/BealC07 fatcat:vhmibtp4e5cazjm6qse4tq545i

Page 1217 of Mathematical Reviews Vol. , Issue 83c [page]

1983 Mathematical Reviews  
Mefas are defined in a manner similar to that of finite automata except that any state can be initial. Unlike finite automata, they cannot be minimised in a unique way.  ...  A rather complete characterization of the relative power of the following features of automata on d-dags is obtained: parallel versus sequential, deterministic versus nondeterministic and finite state  ... 

Fast Computations on Ordered Nominal Sets [article]

David Venhoek, Joshua Moerman, Jurriaan Rot
2020 arXiv   pre-print
We evaluate ONS in two applications: minimisation of automata and active automata learning.  ...  The approach is implemented as the library ONS (Ordered Nominal Sets). Our main motivation is nominal automata, which are models for recognising languages over infinite alphabets.  ...  Nominal automata are defined as ordinary automata by replacing the finite state space and finite alphabet by orbit-finite nominal sets.  ... 
arXiv:1902.08414v2 fatcat:htbgousrenh5pfdmlpcdhng2we

Modelling Fusion Calculus using HD-Automata [chapter]

Gianluigi Ferrari, Ugo Montanari, Emilio Tuosto, Björn Victor, Kidane Yemane
2005 Lecture Notes in Computer Science  
We propose a coalgebraic model of the Fusion calculus based on HD-automata.  ...  Hence, the transition systems of Fusion calculus processes can be minimised according to the notion of observational semantics of the calculus.  ...  On the one hand, given two bisimilar Fusion calculus agents P and Q, if corresponding HD-automata K[P ] and K[Q] are finite, their minimal realisations, sayK[P ] andK[Q], achieved by the minimisation algorithm  ... 
doi:10.1007/11548133_10 fatcat:kl7s4ygd3vbqrabxgbuszfppsy

Minimisation of acyclic deterministic automata in linear time

Dominique Revuz
1992 Theoretical Computer Science  
., Minimisation of acyclic deterministic automata in linear time, Theoretical Computer Science 92 (1992) 181-189. We present a linear algorithm for the minimisation of acyclic deterministic automata.  ...  This algorithm can be used, in particular, on automaton representing lexicons.  ...  Acyclic automata have associated languages that are finite sets of finite words. Two automata are said to be equivalent if and only if they recognise the same language.  ... 
doi:10.1016/0304-3975(92)90142-3 fatcat:65ghlfci25bpvoq5q6z3fimjra

Treatment of Epsilon-Moves in Subset Construction [article]

Gertjan van Noord
1998 arXiv   pre-print
The paper discusses the problem of determinising finite-state automata containing large numbers of epsilon-moves.  ...  Experiments with finite-state approximations of natural language grammars often give rise to very large automata with a very large number of epsilon-moves.  ...  Acknowledgements I am grateful to Mark-Jan Nederhof for support, and for providing me with lots of (often dreadful) automata generated by his finite-state approximation tools.  ... 
arXiv:cmp-lg/9804003v1 fatcat:rysl2xvqwzbqddmsobcwvuxj2e

Minimisation in Logical Form [article]

Nick Bezhanishvili and Marcello Bonsangue and Helle Hvid Hansen and Dexter Kozen and Clemens Kupke and Prakash Panangaden and Alexandra Silva
2020 arXiv   pre-print
Examples include partially observable deterministic finite automata, linear weighted automata viewed as coalgebras over finite-dimensional vector spaces, and belief automata, which are coalgebras on compact  ...  In Bonchi et al. (2014), Brzozowski's double-reversal minimisation algorithm for deterministic finite automata was described categorically and its correctness explained via the duality between reachability  ...  Alternating Automata Alternating finite automata (aka Boolean automata or parallel automata) were first studied in [25, 28, 29, 49, 53] as a finite-state analog of alternating Turing machines.  ... 
arXiv:2005.11551v1 fatcat:v72fxl3yj5dd5gr3qteo6rxvaa

Tree Automata as Algebras: Minimisation and Determinisation [article]

Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, Alexandra Silva
2019 arXiv   pre-print
Under mild assumptions about the base category, we present a general minimisation algorithm for these automata.  ...  We study a categorical generalisation of tree automata, as Σ-algebras for a fixed endofunctor Σ endowed with initial and final states.  ...  If the state space is finite, this construction terminates, yielding the minimisation of the original automaton by Theorem 4.10.  ... 
arXiv:1904.08802v1 fatcat:viekhxtihfcn3jrujycshvroii

Minimising Deterministic Büchi Automata Precisely Using SAT Solving [chapter]

Rüdiger Ehlers
2010 Lecture Notes in Computer Science  
Size reduction of such ω-automata is an important step in probabilistic model checking as well as synthesis of finite-state systems.  ...  We show how deterministic Büchi automata can be fully minimised by reduction to the satisfiability (SAT) problem, yielding the first automated method for this task.  ...  Minimising deterministic Büchi automata Minimising deterministic Büchi automata is different from minimising deterministic automata over finite words: while for the latter, there exists a suitable polynomial  ... 
doi:10.1007/978-3-642-14186-7_28 fatcat:sj422jss4rb3reqs56zctwp4fe

Compression of finite-state automata through failure transitions

Henrik Björklund, Johanna Björklund, Niklas Zechner
2014 Theoretical Computer Science  
., Compression of finite-state automata through failure transitions, Theor. Comput. Sci. (2014), http://dx.  ...  This work investigates the transition-reduction problem for deterministic finite-state automata (DFA). The input is a DFA A and an integer k.  ...  Figure 3 : A pair of finite-state automata for the same language.  ... 
doi:10.1016/j.tcs.2014.09.007 fatcat:4g63q4ix7vfwdikhg2s25j7d34

Minimising Good-for-Games automata is NP complete [article]

Sven Schewe
2020 arXiv   pre-print
be cheaper than minimising deterministic automata.  ...  However, recent work of Radi and Kupferman has shown that minimising Co-Buchi automata with transition based acceptance is tractable, which suggests that the complexity of minimising GFG automata might  ...  a finite state one), but as the ν does not have to be explicit provided, P can be more succinct than a deterministic automaton.  ... 
arXiv:2003.11979v1 fatcat:gzhl6vi7mnf7rcokrphaakaghi

A Formalisation of Finite Automata Using Hereditarily Finite Sets [chapter]

Lawrence C. Paulson
2015 Lecture Notes in Computer Science  
Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode theorem and Brzozowski's minimisation algorithm.  ...  The states of an automaton are HF sets, possibly constructed by product, sum, powerset and similar operations.  ...  Christian Urban and Tobias Nipkow offered advice and comments, and suggested Brzozowski's minimisation algorithm as an example.  ... 
doi:10.1007/978-3-319-21401-6_15 fatcat:rn2m5qu3ujbpxndzkg4owdd6gu

A Formalisation of Finite Automata using Hereditarily Finite Sets [article]

Lawrence C. Paulson
2015 arXiv   pre-print
Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode theorem and Brzozowski's minimisation algorithm.  ...  The states of an automaton are HF sets, possibly constructed by product, sum, powerset and similar operations.  ...  Christian Urban and Tobias Nipkow offered advice, and suggested Brzozowski's minimisation algorithm as an example. The referees made a variety of useful comments.  ... 
arXiv:1505.01662v1 fatcat:wezqpg5of5ehrmngw5oncxggmq
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