scholarly journals On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection

2016 ◽  
pp. 45-59 ◽  
Author(s):  
Rafaela Bastos ◽  
Sabine Broda ◽  
António Machiavelo ◽  
Nelma Moreira ◽  
Rogério Reis
Keyword(s):  
Partial Derivative ◽  
The State ◽  
Regular Expressions ◽  
State Complexity

scholarly journals Regular Expressions with Lookahead

2021 ◽  
Vol 27 (4) ◽  
pp. 324-340
Author(s):  
Martin Berglund ◽  
Brink van der Merwe ◽  
Steyn van Litsenborgh
Keyword(s):  
Finite Automata ◽  
The State ◽  
Regular Expressions ◽  
Deterministic Finite Automata ◽  
State Complexity

This paper investigates regular expressions which in addition to the standard operators of union, concatenation, and Kleene star, have lookaheads. We show how to translate regular expressions with lookaheads (REwLA) to equivalent Boolean automata having at most 3 states more than the length of the REwLA. We also investigate the state complexity when translating REwLA to equivalent deterministic finite automata (DFA).

ON THE AVERAGE STATE COMPLEXITY OF PARTIAL DERIVATIVE AUTOMATA: AN ANALYTIC COMBINATORICS APPROACH

2011 ◽  
Vol 22 (07) ◽  
pp. 1593-1606 ◽  
Author(s):  
SABINE BRODA ◽  
ANTÓNIO MACHIAVELO ◽  
NELMA MOREIRA ◽  
ROGÉRIO REIS
Keyword(s):  
Lower Bound ◽  
Asymptotic Behaviour ◽  
Partial Derivative ◽  
Regular Expression ◽  
Finite Automata ◽  
Regular Expressions ◽  
Alphabet Size ◽  
State Complexity ◽  
Analytic Combinatorics ◽  
Average State

The partial derivative automaton ([Formula: see text]) is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton ([Formula: see text]). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in [Formula: see text] and describe its asymptotic behaviour. This depends on the alphabet size, k, and for growing k's its limit approaches half the number of states in [Formula: see text]. The lower bound corresponds to consider the [Formula: see text] automaton for the marked version of the regular expression, i.e. where all its letters are made different. Experimental results suggest that the average number of states of this automaton, and of the [Formula: see text] automaton for the unmarked regular expression, are very close to each other.

On the state complexity of intersection of regular languages

1991 ◽  
Vol 22 (3) ◽  
pp. 52-54 ◽  
Author(s):  
Sheng Yu ◽  
Qingyu Zhuang
Keyword(s):  
The State ◽  
Regular Languages ◽  
State Complexity

The state complexity of and its connection with temporal logic

1996 ◽  
Vol 58 (4) ◽  
pp. 185-188 ◽  
Author(s):  
Jean-Camille Birget
Keyword(s):  
Temporal Logic ◽  
The State ◽  
State Complexity

scholarly journals State Complexity of Neighbourhoods and Approximate Pattern Matching

2018 ◽  
Vol 29 (02) ◽  
pp. 315-329 ◽  
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Pattern Matching ◽  
Finite Automaton ◽  
The State ◽  
Worst Case ◽  
State Complexity ◽  
Approximate Pattern Matching ◽  
The Given ◽  
Nondeterministic Finite Automaton ◽  
Distance Formula

The neighbourhood of a language [Formula: see text] with respect to an additive distance consists of all strings that have distance at most the given radius from some string of [Formula: see text]. We show that the worst case deterministic state complexity of a radius [Formula: see text] neighbourhood of a language recognized by an [Formula: see text] state nondeterministic finite automaton [Formula: see text] is [Formula: see text]. In the case where [Formula: see text] is deterministic we get the same lower bound for the state complexity of the neighbourhood if we use an additive quasi-distance. The lower bound constructions use an alphabet of size linear in [Formula: see text]. We show that the worst case state complexity of the set of strings that contain a substring within distance [Formula: see text] from a string recognized by [Formula: see text] is [Formula: see text].

scholarly journals Most Complex Non-Returning Regular Languages

2019 ◽  
Vol 30 (06n07) ◽  
pp. 921-957
Author(s):  
Janusz A. Brzozowski ◽  
Sylvie Davies
Keyword(s):  
Star Product ◽  
Upper Bounds ◽  
The State ◽  
Boolean Operations ◽  
Deterministic Finite Automaton ◽  
Initial State ◽  
Complexity Measures ◽  
State Complexity ◽  
Complex Sequence ◽  
Binary Operations

A regular language [Formula: see text] is non-returning if in the minimal deterministic finite automaton accepting it there are no transitions into the initial state. Eom, Han and Jirásková derived upper bounds on the state complexity of boolean operations and Kleene star, and proved that these bounds are tight using two different binary witnesses. They derived tight upper bounds for concatenation and reversal using three different ternary witnesses. These five witnesses use a total of six different transformations. We show that for each [Formula: see text], there exists a ternary witness of state complexity [Formula: see text] that meets the bound for reversal, and restrictions of this witness to binary alphabets meet the bounds for star, product, and boolean operations. Hence all of these operations can be handled simultaneously with a single witness, using only three different transformations. We also derive tight upper bounds on the state complexity of binary operations that take arguments with different alphabets. We prove that the maximal syntactic semigroup of a non-returning language has [Formula: see text] elements and requires at least [Formula: see text] generators. We find the maximal state complexities of atoms of non-returning languages. We show that there exists a most complex sequence of non-returning languages that meet the bounds for all of these complexity measures. Furthermore, we prove there is a most complex sequence that meets all the bounds using alphabets of minimal size.

scholarly journals On the state complexity of closures and interiors of regular languages with subwords and superwords

2016 ◽  
Vol 610 ◽  
pp. 91-107 ◽  
Author(s):  
P. Karandikar ◽  
M. Niewerth ◽  
Ph. Schnoebelen
Keyword(s):  
The State ◽  
Regular Languages ◽  
State Complexity

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.

scholarly journals State Complexity of Suffix Distance

2019 ◽  
Vol 30 (06n07) ◽  
pp. 1197-1216
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Finite Automaton ◽  
Regular Language ◽  
Upper Bounds ◽  
The State ◽  
Deterministic Finite Automaton ◽  
Tight Bound ◽  
State Complexity

The neighbourhood of a regular language with respect to the prefix, suffix and subword distance is always regular and a tight bound for the state complexity of prefix distance neighbourhoods is known. We give upper bounds for the state complexity of the neighbourhood of radius [Formula: see text] of an [Formula: see text]-state deterministic finite automaton language with respect to the suffix distance and the subword distance, respectively. For restricted values of [Formula: see text] and [Formula: see text] we give a matching lower bound for the state complexity of suffix distance neighbourhoods.

STATE COMPLEXITY AND APPROXIMATION

2012 ◽  
Vol 23 (05) ◽  
pp. 1085-1098 ◽  
Author(s):  
YUAN GAO ◽  
SHENG YU
Keyword(s):  
The State ◽  
General Algorithm ◽  
Future Research ◽  
State Complexity ◽  
Combined Operations ◽  
Essential Questions

We discuss a number of essential questions concerning the state complexity research. The questions include why many basic problems were not studied earlier, whether there is a general algorithm for state complexity of combined operations, and whether there is a new and effective approach in this area of research. The concept of state complexity approximation is also discussed. We show that state complexity approximation can be used to obtain good results when the exact state complexities are difficult to find and when the exact state complexities are too complex to comprehend. We also list a number of questions for future research in this area.

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