Upper Bounds on the Imbalance of Discrete Functions Implemented by Sequences of Finite Automata

2019 ◽  
Vol 55 (5) ◽  
pp. 752-759 ◽  
Author(s):  
A. N. Alekseychuk ◽  
S. M. Koniushok ◽  
M. V. Poremskyi
Keyword(s):  
Finite Automata ◽  
Upper Bounds ◽  
Discrete Functions

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

Square on Deterministic, Alternating, and Boolean Finite Automata

2019 ◽  
Vol 30 (06n07) ◽  
pp. 1117-1134
Author(s):  
Galina Jirásková ◽  
Ivana Krajňáková
Keyword(s):  
Upper Bound ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper Bounds ◽  
The State ◽  
Final States ◽  
Deterministic Finite Automaton ◽  
State Complexity

We investigate the state complexity of the square operation on languages represented by deterministic, alternating, and Boolean automata. For each [Formula: see text] such that [Formula: see text], we describe a binary language accepted by an [Formula: see text]-state deterministic finite automaton with [Formula: see text] final states meeting the upper bound [Formula: see text] on the state complexity of its square. We show that in the case of [Formula: see text], the corresponding upper bound cannot be met. Using the binary deterministic witness for square with [Formula: see text] states where half of them are final, we get the tight upper bounds [Formula: see text] and [Formula: see text] on the complexity of the square operation on alternating and Boolean automata, respectively.

On the upper bounds for complexities of discrete functions

2022 ◽  
Author(s):  
Slavcho Shtrakov
Keyword(s):  
Data Structures ◽  
Upper Bounds ◽  
Complexity Measures ◽  
Discrete Functions

In this paper, we study two classes of complexity measures induced by new data structures (abstract reduction systems) for representing [Formula: see text]-valued functions (operations), namely subfunction and minor reductions. When assigning values to some variables in a function, the resulting functions are called subfunctions, and when identifying some variables, the resulting functions are called minors. The number of the distinct objects obtained under these reductions of a function [Formula: see text] is a well-defined measure of complexity denoted by [Formula: see text] and [Formula: see text], respectively. We examine the maximums of these complexities and construct functions which reach these upper bounds.

Nonclosure Properties of Two-Dimensional One-Marker Automata

1997 ◽  
Vol 11 (07) ◽  
pp. 1025-1050 ◽  
Author(s):  
Akira Ito ◽  
Katsushi Inoue ◽  
Yue Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

Operations on Unambiguous Finite Automata

2018 ◽  
Vol 29 (05) ◽  
pp. 861-876 ◽  
Author(s):  
Jozef Jirásek ◽  
Galina Jirásková ◽  
Juraj Šebej
Keyword(s):  
Upper Bound ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper Bounds ◽  
Input String ◽  
State Complexity ◽  
Letter Alphabet ◽  
Left And Right ◽  
Nondeterministic Finite Automaton ◽  
Intersection Formula

A nondeterministic finite automaton is unambiguous if it has at most one accepting computation on every input string. We investigate the state complexity of basic regular operations on languages represented by unambiguous finite automata. We get tight upper bounds for reversal ([Formula: see text]), intersection ([Formula: see text]), left and right quotients ([Formula: see text]), positive closure ([Formula: see text]), star ([Formula: see text]), shuffle ([Formula: see text]), and concatenation ([Formula: see text]). To prove tightness, we use a binary alphabet for intersection and left and right quotients, a ternary alphabet for star and positive closure, a five-letter alphabet for shuffle, and a seven-letter alphabet for concatenation. For complementation, we reduce the trivial upper bound [Formula: see text] to [Formula: see text]. We also get some partial results for union and square.

scholarly journals Improved Upper Bounds for Self-Avoiding Walks in ${\bf Z}^{d}$

10.37236/1499 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
André Pönitz ◽  
Peter Tittmann
Keyword(s):  
Upper Bound ◽  
Finite Automata ◽  
Automatic Generation ◽  
Upper Bounds ◽  
Hypercubic Lattice ◽  
Connective Constant ◽  
Finite Memory ◽  
Self Avoiding Walks

New upper bounds for the connective constant of self-avoiding walks in a hypercubic lattice are obtained by automatic generation of finite automata for counting walks with finite memory. The upper bound in dimension two is 2.679192495.

Operational State Complexity and Decidability of Jumping Finite Automata

2019 ◽  
Vol 30 (01) ◽  
pp. 5-27
Author(s):  
Simon Beier ◽  
Markus Holzer ◽  
Martin Kutrib
Keyword(s):  
Upper Bound ◽  
Open Problem ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper Bounds ◽  
State Complexity ◽  
Semilinear Sets ◽  
Erroneous Result ◽  
Continuous Input ◽  
Regular Sets

We consider jumping finite automata and their operational state complexity and decidability status. Roughly speaking, a jumping automaton is a finite automaton with a non-continuous input. This device has nice relations to semilinear sets and thus to Parikh images of regular sets, which will be exhaustively used in our proofs. In particular, we prove upper bounds on the intersection and complementation. The latter result on the complementation upper bound answers an open problem from [G. J. Lavado, G. Pighizzini, S. Seki: Operational State Complexity of Parikh Equivalence, 2014]. Moreover, we correct an erroneous result on the inverse homomorphism closure. Finally, we also consider the decidability status of standard problems as regularity, disjointness, universality, inclusion, etc. for jumping finite automata.

scholarly journals Improved Upper Bounds for Planarization and Series-Parallelization of Degree-Bounded Graphs

10.37236/2378 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Keith Edwards ◽  
Graham Farr
Keyword(s):  
Finite Automata ◽  
Upper Bounds ◽  
Average Degree ◽  
Regular Expressions ◽  
Connected Graphs ◽  
Deterministic Finite Automata

We study the number of vertices which must be removed from a graph in order to make it planar or series-parallel. We give improved upper bounds on the number of vertices required to planarize graphs of bounded average degree $d$, and for small $d$ also an improved bound for series-parallelization. The coefficient of fragmentability of a class of graphs measures the proportion of vertices that need to be removed from the graphs in the class in order to leave behind bounded sized components. The above bounds on planarization yield improved bounds for the coefficient of fragmentability of the class of connected graphs of average degree at most $d$.As an application we give an improved bound on the size of regular expressions representing deterministic finite automata.

PROVABLY SHORTER REGULAR EXPRESSIONS FROM FINITE AUTOMATA

2013 ◽  
Vol 24 (08) ◽  
pp. 1255-1279 ◽  
Author(s):  
HERMANN GRUBER ◽  
MARKUS HOLZER
Keyword(s):  
Graph Theory ◽  
Finite Automaton ◽  
Regular Expression ◽  
Finite Automata ◽  
Upper Bounds ◽  
Extremal Graph ◽  
Extremal Graph Theory ◽  
Regular Expressions ◽  
Deterministic Finite Automaton

Based on recent results from extremal graph theory, we prove that every n-state binary deterministic finite automaton can be converted into an equivalent regular expression of size O(1.742n) using state elimination. Furthermore, we give improved upper bounds on the language operations intersection and interleaving on regular expressions.

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