An upper bound on the order of locally testable deterministic finite automata

1989 ◽  
pp. 48-65 ◽  
Author(s):  
Sam Kim ◽  
Robert McNaughton ◽  
Robert McCloskey
Keyword(s):  
Upper Bound ◽  
Finite Automata ◽  
Deterministic Finite Automata

STATE COMPLEXITY OF ADDITIVE WEIGHTED FINITE AUTOMATA

2007 ◽  
Vol 18 (06) ◽  
pp. 1407-1416 ◽  
Author(s):  
KAI SALOMAA ◽  
PAUL SCHOFIELD
Keyword(s):  
Upper Bound ◽  
Finite Automaton ◽  
Regular Language ◽  
Finite Automata ◽  
The State ◽  
Deterministic Finite Automata ◽  
State Complexity ◽  
Weighted Finite Automata

It is known that the neighborhood of a regular language with respect to an additive distance is regular. We introduce an additive weighted finite automaton model that provides a conceptually simple way to reprove this result. We consider the state complexity of converting additive weighted finite automata to deterministic finite automata. As our main result we establish a tight upper bound for the state complexity of the conversion.

State Complexity of k-Union and k-Intersection for Prefix-Free Regular Languages

2015 ◽  
Vol 26 (02) ◽  
pp. 211-227 ◽  
Author(s):  
Hae-Sung Eom ◽  
Yo-Sub Han ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Finite Automata ◽  
Constant Factor ◽  
The State ◽  
Regular Languages ◽  
Deterministic Finite Automata ◽  
State Complexity ◽  
Binary Alphabet ◽  
Multiple Intersections

We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alphabet of size k + 1 and for k-intersection using a binary alphabet. We prove that the state complexity upper bound for k-union cannot be reached by languages over an alphabet with less than k symbols. We also give a lower bound construction for k-union using a binary alphabet that is within a constant factor of the upper bound.

THE COMPLEXITY OF DECIDING CODE AND MONOID PROPERTIES FOR REGULAR SETS

1992 ◽  
Vol 02 (01) ◽  
pp. 39-55
Author(s):  
DUNG T. HUYNH
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Finite Automata ◽  
Free Monoid ◽  
Deterministic Finite Automaton ◽  
Deterministic Finite Automata ◽  
Nondeterministic Finite Automata ◽  
Maximal Code ◽  
Regular Sets ◽  
Np Hardness

In this paper, we study the complexity of deciding code and monoid properties for regular sets specified by deterministic or nondeterministic finite automata. The results are as follows. The code problem for regular sets specified by deterministic or nondeterministic finite automata is NL-complete under NC(1) reducibilities. The problems of determining whether a regular set given by a deterministic finite automaton is a monoid or a free monoid or a finitely generated monoid are all NL-complete under NC(1) reducibilities. These monoid problems become PSPACE-complete if the regular sets are specified by nondeterministic finite automata instead. The maximal code problem for deterministic finite automata is shown to be in DET and NL-hard, while a PSPACE upper bound and NP-hardness lower bound hold for the case of nondeterministic finite automata.

COUNTING THE NUMBER OF MINIMAL DFCA OBTAINED BY MERGING STATES

2003 ◽  
Vol 14 (06) ◽  
pp. 995-1006 ◽  
Author(s):  
CEZAR CÂMPEANU ◽  
ANDREI PĂUN
Keyword(s):  
Positive Integer ◽  
Upper Bound ◽  
Finite Automata ◽  
Similarity Relation ◽  
Worst Case ◽  
Deterministic Finite Automata ◽  
Minimization Procedure ◽  
Finite Language ◽  
The Given ◽  
Maximum Expression

Finite Deterministic Cover Automata (DFCA) can be obtained from Deterministic Finite Automata (DFA) using the similarity relation and a method of merging similar states. The DFCA minimization procedure can yield different results depending on the order of merging the similar states, because the minimal DFCA for a finite language is in general not unique. We count the number of minimal DFCA that can be obtained from a given minimal DFA with n states by merging the similar states in the given DFA. We compute an upper-bound for this number and prove that in the worst case, it is n-1 for an unary alphabet, and [Formula: see text] for a non-unary alphabet. We prove that this upper-bound is reached, i.e., for any given positive integer n one can construct a minimal DFA with n states, which has the number of minimal DFCA obtained by merging similar states equal to this maximum expression.

Deterministic finite automata with recursive calls and DPDAs

2003 ◽  
Vol 87 (4) ◽  
pp. 187-193
Author(s):  
Jean H. Gallier ◽  
Salvatore La Torre ◽  
Supratik Mukhopadhyay
Keyword(s):  
Finite Automata ◽  
Deterministic Finite Automata

The detection and stabilisation of limit cycle for deterministic finite automata

2017 ◽  
Vol 91 (4) ◽  
pp. 874-886 ◽  
Author(s):  
Xiaoguang Han ◽  
Zengqiang Chen ◽  
Zhongxin Liu ◽  
Qing Zhang
Keyword(s):  
Limit Cycle ◽  
Finite Automata ◽  
Deterministic Finite Automata

Space-bounded OTMs and REG ∞

Computability ◽  
2021 ◽  
pp. 1-16
Author(s):  
Merlin Carl
Keyword(s):  
Complexity Theory ◽  
Turing Machine ◽  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Logarithmic Space ◽  
Working Space ◽  
Important Theorem

An important theorem in classical complexity theory is that REG = LOGLOGSPACE, i.e., that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs) and show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA, which is a transfinite analogue of LOGLOGSPACE ⊆ REG; the other direction, however, is easily seen to fail.

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