scholarly journals Rabinizer 4: From LTL to Your Favourite Deterministic Automaton

2018 ◽  
pp. 567-577 ◽  
Author(s):  
Jan Křetínský ◽  
Tobias Meggendorfer ◽  
Salomon Sickert ◽  
Christopher Ziegler
Keyword(s):  
Deterministic Automaton

scholarly journals The relaxation normal form of braids is regular

2017 ◽  
Vol 27 (01) ◽  
pp. 61-105
Author(s):  
Vincent Jugé
Keyword(s):  
Normal Form ◽  
Geometric Complexity ◽  
Deterministic Automaton ◽  
Relaxation Algorithm

Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm. We study here this relaxation algorithm and the associated normal form. We prove that this normal form is regular and prefix-closed. We provide an effective construction of a deterministic automaton that recognizes this normal form.

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

2011 ◽  
Vol 22 (02) ◽  
pp. 277-288 ◽  
Author(s):  
MARIE-PIERRE BÉAL ◽  
MIKHAIL V. BERLINKOV ◽  
DOMINIQUE PERRIN
Keyword(s):  
Upper Bound ◽  
The State ◽  
Additional Property ◽  
Prefix Code ◽  
Deterministic Automaton ◽  
Huffman Codes ◽  
Synchronizing Word ◽  
Černý’S Conjecture

Černý's conjecture asserts the existence of a synchronizing word of length at most (n - 1)2 for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p·ar = q·as for some integers r, s (for a state p and a word w, we denote by p·w the state reached from p by the path labeled w). 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(n2). This applies in particular to Huffman codes.

On the length of uncompletable words in unambiguous automata

2019 ◽  
Vol 53 (3-4) ◽  
pp. 115-123
Author(s):  
Antonio Boccuto ◽  
Arturo Carpi
Keyword(s):  
Upper Bound ◽  
Minimal Length ◽  
Deterministic Automaton ◽  
Transformation Monoid

This paper deals with uncomplete unambiguous automata. In this setting, we investigate the minimal length of uncompletable words. This problem is connected with a well-known conjecture formulated by A. Restivo. We introduce the notion of relatively maximal row for a suitable monoid of matrices. We show that, if M is a monoid of {0, 1}-matrices of dimension n generated by a set S, then there is a matrix of M containing a relatively maximal row which can be expressed as a product of O(n3) matrices of S. As an application, we derive some upper bound to the minimal length of an uncompletable word of an uncomplete unambiguous automaton, in the case that its transformation monoid contains a relatively maximal row which is not maximal. Finally we introduce the maximal row automaton associated with an unambiguous automaton A. It is a deterministic automaton, which is complete if and only if A is. We prove that the minimal length of the uncompletable words of A is polynomially bounded by the number of states of A and the minimal length of the uncompletable words of the associated maximal row automaton.

LINEAR-TIME PRIME DECOMPOSITION OF REGULAR PREFIX CODES

2003 ◽  
Vol 14 (06) ◽  
pp. 1019-1031 ◽  
Author(s):  
JUREK CZYZOWICZ ◽  
WOJCIECH FRACZAK ◽  
ANDRZEJ PELC ◽  
WOJCIECH RYTTER
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Prefix Code ◽  
Prime Decomposition ◽  
Deterministic Automaton ◽  
Prefix Codes ◽  
Efficient Storage ◽  
Finite State ◽  
Infinite Set

One of the new approaches to data classification uses prefix codes and finite state automata as representations of prefix codes. A prefix code is a (possibly infinite) set of strings such that no string is a prefix of another one. An important task driven by the need for the efficient storage of such automata in memory is the decomposition (in the sense of formal languages concatenation) of prefix codes into prime factors. We investigate properties of such prefix code decompositions. A prime decomposition is a decomposition of a prefix code into a concatenation of nontrivial prime prefix codes. A prefix code is prime if it cannot be decomposed into at least two nontrivial prefix codes. In the paper a linear time algorithm is designed which finds the prime decomposition F1F2…Fk of a regular prefix code F given by its minimal deterministic automaton. Our results are especially interesting for infinite regular prefix codes.

Exact Searching for the Smallest Deterministic Automaton

2021 ◽  
pp. 50-63
Author(s):  
Wojciech Wieczorek ◽  
Łukasz Strąk ◽  
Arkadiusz Nowakowski ◽  
Olgierd Unold
Keyword(s):  
Deterministic Automaton

scholarly journals Decidability of regular language genus computation

2019 ◽  
Vol 29 (9) ◽  
pp. 1428-1443
Author(s):  
Guillaume Bonfante ◽  
Florian L. Deloup
Keyword(s):  
Regular Language ◽  
New Genus ◽  
Regular Languages ◽  
Minimal Size ◽  
Deterministic Automaton ◽  
Letter Alphabet ◽  
New Family ◽  
Generic Class ◽  
Deterministic Automata ◽  
The Difference

AbstractThis article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of |L|gen to be the minimal size of all finite deterministic automata of genus g(L) computing L.We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size |L|gen can grow at least exponentially in size |L|. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genus-based hierarchies of regular languages and in particular, we show a new family of regular languages on a two-letter alphabet having arbitrary high genus.

scholarly journals A description based on languages of the final non-deterministic automaton

2014 ◽  
Vol 536 ◽  
pp. 1-20 ◽  
Author(s):  
A. Ballester-Bolinches ◽  
E. Cosme-Llópez ◽  
R. Esteban-Romero
Keyword(s):  
Deterministic Automaton

scholarly journals An nlogn algorithm for hyper-minimizing a (minimized) deterministic automaton

2010 ◽  
Vol 411 (38-39) ◽  
pp. 3404-3413 ◽  
Author(s):  
Markus Holzer ◽  
Andreas Maletti
Keyword(s):  
Deterministic Automaton
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