Learning Regular Languages Using Nondeterministic Finite Automata

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.

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NONDETERMINISTIC DESCRIPTIONAL COMPLEXITY OF REGULAR LANGUAGES

International Journal of Foundations of Computer Science ◽

10.1142/s0129054103002199 ◽

2003 ◽

Vol 14 (06) ◽

pp. 1087-1102 ◽

Cited By ~ 100

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.

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DESCRIPTIONAL COMPLEXITY OF NFA OF DIFFERENT AMBIGUITY

International Journal of Foundations of Computer Science ◽

10.1142/s0129054105003418 ◽

2005 ◽

Vol 16 (05) ◽

pp. 975-984 ◽

Cited By ~ 36

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).

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DESCRIPTIONAL COMPLEXITY OF SPLICING SYSTEMS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054108005978 ◽

2008 ◽

Vol 19 (04) ◽

pp. 813-826 ◽

Cited By ~ 6

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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OPTIMAL SIMULATIONS OF WEAK RESTARTING AUTOMATA

International Journal of Foundations of Computer Science ◽

10.1142/s0129054108005966 ◽

2008 ◽

Vol 19 (04) ◽

pp. 795-811 ◽

Cited By ~ 2

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.

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Enumerating the strings of regular languages

Journal of Functional Programming ◽

10.1017/s0956796803004982 ◽

2004 ◽

Vol 14 (5) ◽

pp. 503-518 ◽

Cited By ~ 6

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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