OPTIMAL SIMULATIONS OF WEAK RESTARTING AUTOMATA

2008 ◽  
Vol 19 (04) ◽  
pp. 795-811 ◽  
Author(s):  
MARTIN KUTRIB ◽  
JENS REIMANN
Keyword(s):  
Upper Bound ◽  
Finite Automata ◽  
Regular Languages ◽  
Complete Picture ◽  
Nondeterministic Finite Automata ◽  
Trade Offs

The simulation of weak restarting automata, i.e., classical restarting automata accepting exactly the regular languages, by finite automata is studied. Some of the trade-offs in the number of states when changing the representation are known. Here we continue the investigation in order to draw an almost complete picture of the descriptional power gained in the additional structural resources of weak restarting automata. In particular, for det-RR(1)-simulations of nondeterministic finite automata we obtain the same tight bounds as for simulations of R(1)-automata, though in some cases the latter class is much more efficient than the former. Moreover, the DFA-simulation of det-RR(1)-automata is considered. The shown bounds are of factorial order and are tight. The constructions are via alternating finite automata to DFAs. So, in addition, an upper bound for the AFA-simulation is obtained.

scholarly journals Nondeterministic Syntactic Complexity

2021 ◽  
pp. 448-468
Author(s):  
Robert S. R. Myers ◽  
Stefan Milius ◽  
Henning Urbat
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Syntactic Complexity ◽  
Deterministic Finite Automata ◽  
Syntactic Monoid ◽  
Nondeterministic Finite Automata ◽  
Structural Work ◽  
Algebraic Interpretation ◽  
Nondeterministic State

AbstractWe introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the ‘canonical boolean representation’ of the syntactic monoid. Equivalently, it is the least number of states of any subatomic nondeterministic acceptor. It turns out that essentially all previous structural work on nondeterministic state-minimality computes this measure. Our approach rests on an algebraic interpretation of nondeterministic finite automata as deterministic finite automata endowed with semilattice structure. Crucially, the latter form a self-dual category.

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.

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).

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.

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.

The complexity of concatenation on deterministic and alternating finite automata

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 153-168
Author(s):  
Michal Hospodár ◽  
Galina Jirásková
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Open Problem ◽  
Finite Automata ◽  
The State ◽  
Regular Languages ◽  
Final States ◽  
State Complexity ◽  
Deterministic Automata

We study the state complexity of the concatenation operation on regular languages represented by deterministic and alternating finite automata. For deterministic automata, we show that the upper bound m2n − k2n−1 on the state complexity of concatenation can be met by ternary languages, the first of which is accepted by an m-state DFA with k final states, and the second one by an n-state DFA with ℓ final states for arbitrary integers m, n, k, ℓ with 1 ≤ k ≤ m − 1 and 1 ≤ ℓ ≤ n − 1. In the case of k ≤ m − 2, we are able to provide appropriate binary witnesses. In the case of k = m − 1 and ℓ ≥ 2, we provide a lower bound which is smaller than the upper bound just by one. We use our binary witnesses for concatenation on deterministic automata to describe binary languages meeting the upper bound 2m + n + 1 for the concatenation on alternating finite automata. This solves an open problem stated by Fellah et al. [Int. J. Comput. Math. 35 (1990) 117–132].

scholarly journals Enumerating the strings of regular languages

2004 ◽  
Vol 14 (5) ◽  
pp. 503-518 ◽  
Author(s):  
M. DOUGLAS McILROY
Keyword(s):  
Regular Expression ◽  
Finite Automata ◽  
Standard Form ◽  
Regular Languages ◽  
Nondeterministic Finite Automata ◽  
Set Operations

Haskell code is developed for two ways to list the strings of the language defined by a regular expression: directly by set operations and indirectly by converting to and simulating an equivalent automaton. The exercise illustrates techniques for dealing with infinite ordered domains and leads to an effective standard form for nondeterministic finite automata.

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