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).

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.

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.

scholarly journals The Size of One-Way Cellular Automata

2010 ◽  
Vol DMTCS Proceedings vol. AL,... (Proceedings) ◽  
Author(s):  
Martin Kutrib ◽  
Jonas Lefèvre ◽  
Andreas Malcher
Keyword(s):  
Cellular Automata ◽  
Real Time ◽  
Finite Automata ◽  
Fixed Number ◽  
Point Of View ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Order Of Magnitude ◽  
International Audience ◽  
Number Of Cells

International audience We investigate the descriptional complexity of basic operations on real-time one-way cellular automata with an unbounded as well well as a fixed number of cells. The size of the automata is measured by their number of states. Most of the bounds shown are tight in the order of magnitude, that is, the sizes resulting from the effective constructions given are optimal with respect to worst case complexity. Conversely, these bounds also show the maximal savings of size that can be achieved when a given minimal real-time OCA is decomposed into smaller ones with respect to a given operation. From this point of view the natural problem of whether a decomposition can algorithmically be solved is studied. It turns out that all decomposition problems considered are algorithmically unsolvable. Therefore, a very restricted cellular model is studied in the second part of the paper, namely, real-time one-way cellular automata with a fixed number of cells. These devices are known to capture the regular languages and, thus, all the problems being undecidable for general one-way cellular automata become decidable. It is shown that these decision problems are $\textsf{NLOGSPACE}$-complete and thus share the attractive computational complexity of deterministic finite automata. Furthermore, the state complexity of basic operations for these devices is studied and upper and lower bounds are given.

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 Finite automata with undirected state graphs

2021 ◽  
Author(s):  
Martin Kutrib ◽  
Andreas Malcher ◽  
Christian Schneider
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Deterministic Case ◽  
Boolean Operations ◽  
State Complexity ◽  
Descriptional Complexity ◽  
Language Classes ◽  
Different Types ◽  
State Graphs

AbstractWe investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then, the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.

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.

NONDETERMINISTIC BIAUTOMATA AND THEIR DESCRIPTIONAL COMPLEXITY

2014 ◽  
Vol 25 (07) ◽  
pp. 837-855
Author(s):  
MARKUS HOLZER ◽  
SEBASTIAN JAKOBI
Keyword(s):  
Head Movement ◽  
Blow Up ◽  
Finite Automata ◽  
Regular Languages ◽  
Regular Expressions ◽  
Descriptional Complexity

We investigate the descriptional complexity of nondeterministic biautomata, which are a generalization of biautomata [O. KLÍMA, L. POLÁK: On biautomata. RAIRO — Theor. Inf. Appl., 46(4), 2012]. Simply speaking, biautomata are finite automata reading the input from both sides; although the head movement is nondeterministic, additional requirements enforce biautomata to work deterministically. First we study the size blow-up when determinizing nondeterministic biautomata. Further, we give tight bounds on the number of states for nondeterministic biautomata accepting regular languages relative to the size of ordinary finite automata, regular expressions, and syntactic monoids. It turns out that as in the case of ordinary finite automata nondeterministic biautomata are superior to biautomata with respect to their relative succinctness in representing regular languages.

Sign in / Sign up

Export Citation Format

Share Document