Descriptional complexity of regular languages

2021 ◽  
pp. 411-457
Author(s):  
Hermann Gruber ◽  
Markus Holzer ◽  
Martin Kutrib
Keyword(s):  
Regular Languages ◽  
Descriptional Complexity

scholarly journals Descriptional Complexity of Bounded Regular Languages

2016 ◽  
pp. 138-152 ◽  
Author(s):  
Andrea Herrmann ◽  
Martin Kutrib ◽  
Andreas Malcher ◽  
Matthias Wendlandt
Keyword(s):  
Regular Languages ◽  
Descriptional Complexity

The complexity of weakly recognizing morphisms

2018 ◽  
Vol 53 (1-2) ◽  
pp. 1-17
Author(s):  
Lukas Fleischer ◽  
Manfred Kufleitner
Keyword(s):  
Computational Complexity ◽  
Regular Languages ◽  
Decision Problems ◽  
Membership Problem ◽  
Surjective Morphism ◽  
Infinite Words ◽  
Descriptional Complexity ◽  
Emptiness Problem ◽  
Free Semigroups ◽  
Büchi Automaton

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We study the descriptional complexity of various constructions and the computational complexity of various decision problems for weakly recognizing morphisms. The constructions we consider are the conversion from and to Büchi automata, the conversion into strongly recognizing morphisms, as well as complementation. We also show that the fixed membership problem is NC1-complete, the general membership problem is in L and that the inclusion, equivalence and universality problems are NL-complete. The emptiness problem is shown to be NL-complete if the input is given as a non-surjective morphism.

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 On the Expressive Power of Stateless Ordered Restart-Delete Automata

2021 ◽  
Author(s):  
Friedrich Otto
Keyword(s):  
Expressive Power ◽  
Single Letter ◽  
Regular Languages ◽  
Descriptional Complexity ◽  
Context Free

AbstractStateless ordered restart-delete automata (stl-ORD-automata) are studied. These are obtained from the stateless ordered restarting automata (stl-ORWW-automata) by introducing an additional restart-delete operation, which, based on the surrounding context, deletes a single letter. While the stl-ORWW-automata accept the regular languages, we show that the swift stl-ORD-automata yield a characterization for the class of context-free languages. Here a stl-ORD-automaton is called swift if it can move its window to any position after performing a restart. We also study the descriptional complexity of swift stl-ORD-automata and relate them to limited context restarting automata.

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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