More on the Descriptional Complexity of Products of Finite Automata

2021 ◽  
pp. 76-87
Author(s):  
Markus Holzer ◽  
Christian Rauch
Keyword(s):  
Finite Automata ◽  
Descriptional Complexity

Descriptional Complexity of the Forever Operator

2019 ◽  
Vol 30 (01) ◽  
pp. 115-134 ◽  
Author(s):  
Michal Hospodár ◽  
Galina Jirásková ◽  
Peter Mlynárčik
Keyword(s):  
Regular Language ◽  
Finite Automata ◽  
Deterministic Finite Automata ◽  
State Complexity ◽  
Descriptional Complexity ◽  
Trade Offs ◽  
Number Formula ◽  
Deterministic Automata ◽  
Initial States ◽  
Nondeterministic State

We examine the descriptional complexity of the forever operator, which assigns the language [Formula: see text] to a regular language [Formula: see text], and we investigate the trade-offs between various models of finite automata. We consider complete and partial deterministic finite automata, nondeterministic finite automata with single or multiple initial states, alternating, and Boolean finite automata. We assume that the argument and the result of this operation are accepted by automata belonging to one of these six models. We investigate all possible trade-offs and provide a tight upper bound for 32 of 36 of them. The most interesting result is the trade-off from nondeterministic to deterministic automata given by the Dedekind number [Formula: see text]. We also prove that the nondeterministic state complexity of [Formula: see text] is [Formula: see text] which solves an open problem stated by Birget [The state complexity of [Formula: see text] and its connection with temporal logic, Inform. Process. Lett. 58 (1996) 185–188].

THE COMPLEXITY OF REGULAR(-LIKE) EXPRESSIONS

2011 ◽  
Vol 22 (07) ◽  
pp. 1533-1548 ◽  
Author(s):  
MARKUS HOLZER ◽  
MARTIN KUTRIB
Keyword(s):  
Computational Complexity ◽  
Finite Automata ◽  
Regular Expressions ◽  
Descriptional Complexity

We summarize results on the complexity of regular(-like) expressions and tour a fragment of the literature. In particular we focus on the descriptional complexity of the conversion of regular expressions to equivalent finite automata and vice versa, to the computational complexity of problems on regular-like expressions such as, e.g., membership, inequivalence, and non-emptiness of complement, and finally on the operation problem measuring the required size for transforming expressions with additional language operations (built-in or not) into equivalent ordinary regular expressions.

scholarly journals NONDETERMINISTIC DESCRIPTIONAL COMPLEXITY OF REGULAR LANGUAGES

2003 ◽  
Vol 14 (06) ◽  
pp. 1087-1102 ◽  
Author(s):  
MARKUS HOLZER ◽  
MARTIN KUTRIB
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Boolean Operations ◽  
Worst Case ◽  
Descriptional Complexity ◽  
Exact Number ◽  
Nondeterministic Finite Automata ◽  
Order Of Magnitude

We investigate the descriptional complexity of operations on finite and infinite regular languages over unary and arbitrary alphabets. The languages are represented by nondeterministic finite automata (NFA). In particular, we consider Boolean operations, catenation operations – concatenation, iteration, λ-free iteration – and the reversal. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. Otherwise tight bounds in the order of magnitude are shown.

DESCRIPTIONAL COMPLEXITY OF NFA OF DIFFERENT AMBIGUITY

2005 ◽  
Vol 16 (05) ◽  
pp. 975-984 ◽  
Author(s):  
HING LEUNG
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Descriptional Complexity ◽  
Nondeterministic Finite Automata ◽  
Initial States

In this paper, we study the tradeoffs in descriptional complexity of NFA (nondeterministic finite automata) of various amounts of ambiguity. We say that two classes of NFA are separated if one class can be exponentially more succinct in descriptional sizes than the other. New results are given for separating DFA (deterministic finite automata) from UFA (unambiguous finite automata), UFA from MDFA (DFA with multiple initial states) and UFA from FNA (finitely ambiguous NFA). We present a family of regular languages that we conjecture to be a good candidate for separating FNA from LNA (linearly ambiguous NFA).

scholarly journals Descriptional Complexity of Semi-Simple Splicing Systems

2021 ◽  
pp. 1-27
Author(s):  
Lila Kari ◽  
Timothy Ng
Keyword(s):  
Regular Language ◽  
Biological Process ◽  
Finite Automata ◽  
Dna Recombination ◽  
The Other ◽  
Binary String ◽  
Deterministic Finite Automata ◽  
Descriptional Complexity ◽  
Generative Mechanisms ◽  
Splicing Systems

Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the “splicing operation”, a cut-and-paste binary string operation defined by a set of “splicing rules”, quadruples [Formula: see text] where [Formula: see text] are words over an alphabet [Formula: see text]. For two strings [Formula: see text] and [Formula: see text], applying the splicing rule [Formula: see text] produces the string [Formula: see text]. In this paper we focus on a particular type of splicing systems, called [Formula: see text] semi-simple splicing systems, [Formula: see text] and [Formula: see text], wherein all splicing rules [Formula: see text] have the property that the two strings in positions [Formula: see text] and [Formula: see text] in [Formula: see text] are singleton letters, while the other two strings are empty. The language generated by such a system consists of the set of words that are obtained starting from an initial set called “axiom set”, by iteratively applying the splicing rules to strings in the axiom set as well as to intermediately produced strings. We consider semi-simple splicing systems where the axiom set is a regular language, and investigate the descriptional complexity of such systems in terms of the size of the minimal deterministic finite automata that recognize the languages they generate.

DESCRIPTIONAL COMPLEXITY OF SPLICING SYSTEMS

2008 ◽  
Vol 19 (04) ◽  
pp. 813-826 ◽  
Author(s):  
REMCO LOOS ◽  
ANDREAS MALCHER ◽  
DETLEF WOTSCHKE
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Regular Languages ◽  
Upper And Lower Bounds ◽  
Descriptional Complexity ◽  
Nondeterministic Finite Automata ◽  
Total Length ◽  
Splicing Systems

In this paper, the descriptional complexity of extended finite splicing systems is studied. These systems are known to generate exactly the class of regular languages. Upper and lower bounds are shown relating the size of these splicing systems, defined as the total length of the rules and the initial language of the system, to the size of their equivalent minimal nondeterministic finite automata (NFA). In addition, an accepting model of extended finite splicing systems is studied. Using this variant one can obtain systems which are more than polynomially more succinct than the equivalent NFA or generating extended finite splicing system.

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