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Synchronizing non-deterministic finite automata [article]

Henk Don, Hans Zantema
2017 arXiv   pre-print
In this paper, we show that every D3-directing CNFA can be mapped uniquely to a DFA with the same synchronizing word length.  ...  Introduction and preliminaries In this paper we study synchronization of non-deterministic finite automata (NFAs).  ...  Formally, a complete non-deterministic finite automaton (CNFA) A over a finite alphabet Σ consists of a finite set Q of states and a map δ : Q × Σ → 2 Q \ {∅}.  ... 
arXiv:1703.07995v1 fatcat:5bd3roxlkfgdjgk3gib5gu5kxu

Synchronizing Words for Weighted and Timed Automata

Laurent Doyen, Line Juhl, Kim G. Larsen, Nicolas Markey, Mahsa Shirmohammadi, Marc Herbstritt
2014 Foundations of Software Technology and Theoretical Computer Science  
For timed automata the synchronization problems are shown to be PSPACE-complete in the deterministic case, and undecidable in the non-deterministic case.  ...  We consider the synchronization problem in several variants and combinations of these, including deterministic and non-deterministic timed and weighted automata, synchronization to unique location with  ...  Synchronizing automata have classically been studied in the setting of complete deterministic finite-state automata, with polynomial bounds on the length of the shortest synchronizing word [3] and the  ... 
doi:10.4230/lipics.fsttcs.2014.121 dblp:conf/fsttcs/0001JLMS14 fatcat:fmqev4scsbgrlcmc2rjdlot4ly

Synchronization of Pushdown Automata [chapter]

Didier Caucal
2006 Lecture Notes in Computer Science  
The pushdown automata synchronized by a given transducer accept languages which form an effective boolean algebra containing the regular languages and included in the deterministic real-time context-free  ...  The visibly pushdown automata are the automata synchronized by an one state transducer whose output labels are −1, 0, 1.  ...  So we restrict any graph grammar to be deterministic : there is only one rule per non-terminal.  ... 
doi:10.1007/11779148_12 fatcat:5n3xu55gqjcrjl3uodfmzatsf4

LR(0) Conjunctive Grammars and Deterministic Synchronized Alternating Pushdown Automata [chapter]

Tamar Aizikowitz, Michael Kaminski
2011 Lecture Notes in Computer Science  
In this paper we introduce a sub-family of synchronized alternating pushdown automata, Deterministic Synchronized Alternating Pushdown Automata, and a sub-family of conjunctive grammars, LR(0) Conjunctive  ...  We prove that deterministic SAPDA and LR(0) conjunctive grammars have the same recognition/generation power, analogously to the classical equivalence between acceptance by empty stack of deterministic  ...  Synchronized Alternating Pushdown Automata (SAPDA), introduced in [1], are a weakened version of Alternating Pushdown Automata, which, in particular, accept intersections of context-free languages.  ... 
doi:10.1007/978-3-642-20712-9_27 fatcat:kjzxt5mluzbgrjoaogzyxpnb2a

A QUADRATIC UPPER BOUND ON THE SIZE OF A SYNCHRONIZING WORD IN ONE-CLUSTER AUTOMATA

MARIE-PIERRE BÉAL, MIKHAIL V. BERLINKOV, DOMINIQUE PERRIN
2011 International Journal of Foundations of Computer Science  
Cerný's conjecture asserts the existence of a synchronizing word of length at most (n − 1) 2 for any synchronized n-state deterministic automaton.  ...  As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n 2 ). This applies in particular to Huffman codes.  ...  Introduction Synchronized automata are deterministic and complete finite-state automata admitting a synchronizing word, that is a word which takes each state of the automaton to a single special state.Černý  ... 
doi:10.1142/s0129054111008039 fatcat:yh4p4wtzobf7ve47ig42lvjggi

PARTIALLY ORDERED TWO-WAY BÜCHI AUTOMATA

MANFRED KUFLEITNER, ALEXANDER LAUSER
2011 International Journal of Foundations of Computer Science  
As for finite words, the nondeterministic variant recognizes the fragment Σ 2 of first-order logic FO[<] and the deterministic version yields the ∆ 2 -definable ω-languages.  ...  As a byproduct of our results, we show that deterministic partially ordered two-way Büchi automata are effectively closed under Boolean operations.  ...  Hence, non-inclusion can be verified in NP, i.e., Inclusion is in coNP. Lemma 5 Emptiness is coNP-hard for deterministic po2-Büchi automata.  ... 
doi:10.1142/s0129054111009082 fatcat:7sndiflwirafjd7me7tz4ieqvm

On the bound of the synchronization delay of a local automaton

Marie-Pierre Béal, Jean Senellart
1998 Theoretical Computer Science  
It has been conjectured by Kim et al. (1991) that, for deterministic local automata, it is O(N") on a twoletter alphabet and no less than O(N2) in the general case.  ...  The synchronization delay of an N-state local automaton is known to be 0(N2).  ...  For a deterministic automaton, we call a non-synchronizing sequence a finite word u such that there are two paths labeled by U, (pi, ai,pi+t)s<j<k_t and (pi, ai, p:+,)~~i~k_l, with pl # pi for all indices  ... 
doi:10.1016/s0304-3975(98)80011-x fatcat:c24wqk4hdncejkhpb7tsmxlt3i

Partially Ordered Two-Way Büchi Automata [chapter]

Manfred Kufleitner, Alexander Lauser
2011 Lecture Notes in Computer Science  
As an intermediate step, we show that deterministic partially ordered two-way B\"uchi automata are effectively closed under Boolean operations.  ...  Our main contribution is that deterministic partially ordered two-way B\"uchi automata are expressively complete for the first-order fragment Delta2.  ...  Hence, non-inclusion can be verified in NP, i.e., Inclusion is in coNP. Lemma 5 Emptiness is coNP-hard for deterministic po2-Büchi automata.  ... 
doi:10.1007/978-3-642-18098-9_20 fatcat:zcncfcrr4fezxaazpoamaae6ue

Synchronizing Deterministic Push-Down Automata Can Be Really Hard

Henning Fernau, Petra Wolf, Tomoyuki Yamakami, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
In this paper, we extend this algorithmic question to deterministic automata beyond finite automata.  ...  The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time.  ...  In this work, we want to move away from deterministic finite automata to more general deterministic push-down automata. What should a synchronizing word mean in this context?  ... 
doi:10.4230/lipics.mfcs.2020.33 dblp:conf/mfcs/Fernau0Y20 fatcat:flms4ccytnac7bdu5ljex26dha

A Quadratic Upper Bound on the Size of a Synchronizing Word in One-Cluster Automata [chapter]

Marie-Pierre Béal, Dominique Perrin
2009 Lecture Notes in Computer Science  
Černý's conjecture asserts the existence of a synchronizing word of length at most (n − 1) 2 for any synchronized n-state deterministic automaton.  ...  As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n 2 ). This applies in particular to Huffman codes.  ...  Introduction Synchronized automata are deterministic and complete finite-state automata admitting a synchronizing word, that is a word which takes each state of the automaton to a single special state.Černý  ... 
doi:10.1007/978-3-642-02737-6_6 fatcat:qq2yn2afsvgilp6u5dejrecbba

Page 1163 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
Moreover, he presents criteria for the class of realizations of a non- deterministic automaton to be empty, a single element or finite. 68Q Theory of computing 98b:68127 Since nondeterministic automata  ...  He obtains, by using the apparatus of realizations, a criterion for finiteness of the class of weakly initial deterministic automata.  ... 

Sofic and Almost of Finite Type Tree-Shifts [chapter]

Nathalie Aubrun, Marie-Pierre Béal
2010 Lecture Notes in Computer Science  
We show that, contrary to shifts of infinite sequences, there is no unique minimal deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized  ...  We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite trees accepted by finite tree automata.  ...  A deterministic tree automaton which has a synchronizing block is called synchronized. Minimal deterministic tree automata Let X be a tree-shift. A context c is a finite pattern with a marked leaf.  ... 
doi:10.1007/978-3-642-13182-0_2 fatcat:rpldmdx7zbeplpbqwf7vosqm64

Boolean Algebras from Trace Automata

Alexandre Mansard, Michael Wagner
2019 Foundations of Software Technology and Theoretical Computer Science  
We consider trace automata. Their vertices are Mazurkiewicz traces and they accept finite words.  ...  We show that if a family F of trace automata is closed under these operations, then for any deterministic automaton H ∈ F, the word languages accepted by the deterministic automata of F that are length-reducible  ...  If two deterministic automata are length-reducible to a same deterministic one, then their level-length synchronization is also a deterministic automaton. By Lemma 1, L(G H) ⊆ L(H).  ... 
doi:10.4230/lipics.fsttcs.2019.48 dblp:conf/fsttcs/Mansard19 fatcat:e63hljkjufg4dbenrunpj3zfgu

A Survey of Multi-Tape Automata [article]

Carlo A. Furia
2013 arXiv   pre-print
It also includes an original algorithm for the intersection of one-way nondeterministic finite-state automata.  ...  This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes.  ...  Correspondingly, NFA(n, s, r) denotes the class of s-synchronized r-reversal bounded n-tape two-way nondeterministic finite-state automata, DFA(n, s, r) the corresponding deterministic class, and when  ... 
arXiv:1205.0178v2 fatcat:gotm4g3mzvg7zhssfnsvpy72he

Page 6943 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
alternating finite automata.  ...  finite automata (note that alternating finite automata recognize only regular languages [A.  ... 
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