scholarly journals An Approximate Method for Calculating the Distance Between Regular Languages for Multitape Finite Automata

2020 ◽  
pp. 69-79
Author(s):  
Tigran Grigoryan
Keyword(s):  
Approximate Method ◽  
Metric Space ◽  
Finite Automata ◽  
Regular Languages ◽  
Regular Expressions

Sets of word tuples, accepted by multitape finite automata and a metric space for languages accepted by these automata, are considered. These languages are represented using the same notation as the known notation of regular expressions for languages accepted by one-tape automata. The only difference is the interpretation of the ”concatenation” operation in the notation. An algorithm is proposed for calculating the introduced distance between regular languages accepted by multitape finite automata.

COMPLEXITY IN UNION-FREE REGULAR LANGUAGES

2011 ◽  
Vol 22 (07) ◽  
pp. 1639-1653 ◽  
Author(s):  
GALINA JIRÁSKOVÁ ◽  
TOMÁŠ MASOPUST
Keyword(s):  
Free Path ◽  
Finite Automata ◽  
Regular Languages ◽  
Regular Expressions ◽  
Deterministic Finite Automata ◽  
Union Operation

We continue the investigation of union-free regular languages that are described by regular expressions without the union operation. We also define deterministic union-free languages as languages accepted by one-cycle-free-path deterministic finite automata, and show that they are properly included in the class of union-free languages. We prove that (deterministic) union-freeness of languages does not accelerate regular operations, except for the reversal in the nondeterministic case.

Union-Freeness Revisited — Between Deterministic and Nondeterministic Union-Free Languages

2021 ◽  
pp. 1-23
Author(s):  
Benedek Nagy
Keyword(s):  
Normal Form ◽  
Regular Language ◽  
Regular Expression ◽  
Finite Automata ◽  
Finite Union ◽  
Regular Languages ◽  
Regular Expressions ◽  
Closure Properties ◽  
Language Class ◽  
Union Operation

Union-free expressions are regular expressions without using the union operation. Consequently, (nondeterministic) union-free languages are described by regular expressions using only concatenation and Kleene star. The language class is also characterised by a special class of finite automata: 1CFPAs have exactly one cycle-free accepting path from each of their states. Obviously such an automaton has exactly one accepting state. The deterministic counterpart of such class of automata defines the deterministic union-free (d-union-free, for short) languages. In this paper [Formula: see text]-free nondeterministic variants of 1CFPAs are used to define n-union-free languages. The defined language class is shown to be properly between the classes of (nondeterministic) union-free and d-union-free languages (in case of at least binary alphabet). In case of unary alphabet the class of n-union-free languages coincides with the class of union-free languages. Some properties of the new subregular class of languages are discussed, e.g., closure properties. On the other hand, a regular expression is in union normal form if it is a finite union of union-free expressions. It is well known that every regular expression can be written in union normal form, i.e., all regular languages can be described as finite unions of (nondeterministic) union-free languages. It is also known that the same fact does not hold for deterministic union-free languages, that is, there are regular languages that cannot be written as finite unions of d-union-free languages. As an important result here we show that every regular language can be defined by a finite union of n-union-free languages. This fact also allows to define n-union-complexity of regular languages.

scholarly journals An Fuzzy Lexical Research

2019 ◽  
Vol 8 (6S3) ◽  
pp. 1209-1211
Keyword(s):  
Finite Automata ◽  
String Matching ◽  
Regular Languages ◽  
Regular Expressions ◽  
Lexical Analysis ◽  
Design And Implementation ◽  
Comprehensive View ◽  
Analysis Phase ◽  
Source Program ◽  
Degree Of Membership

The objective of this paper is to analyse the design and implementation of the fuzzy lexical analyser and observe how it is different from the traditional lexical analyser. It is known that lexical analysis is an important phase of a compiler. It reads the source program character by character and uses regular expressions, finite automata methods for string matching. Unlike traditional lexical analysers, tokens in fuzzy analysers belong to more than one token type with varying degree of membership. The paper exchange views on the design and implementation of fuzzy lexical analysers. It observes algorithms that handle errors due to insertion, deletion etc. in the lexical analysis phase of a compiler. Several properties of fuzzy languages are also reviewed. Hence this paper gives a comprehensive view of fuzzy regular languages, models and algorithms

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.

Space-bounded OTMs and REG ∞

Computability ◽  
2021 ◽  
pp. 1-16
Author(s):  
Merlin Carl
Keyword(s):  
Complexity Theory ◽  
Turing Machine ◽  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Finite Automata ◽  
Logarithmic Space ◽  
Working Space ◽  
Important Theorem

An important theorem in classical complexity theory is that REG = LOGLOGSPACE, i.e., that languages decidable with double-logarithmic space bound are regular. We consider a transfinite analogue of this theorem. To this end, we introduce deterministic ordinal automata (DOAs) and show that they satisfy many of the basic statements of the theory of deterministic finite automata and regular languages. We then consider languages decidable by an ordinal Turing machine (OTM), introduced by P. Koepke in 2005 and show that if the working space of an OTM is of strictly smaller cardinality than the input length for all sufficiently long inputs, the language so decided is also decidable by a DOA, which is a transfinite analogue of LOGLOGSPACE ⊆ REG; the other direction, however, is easily seen to fail.

scholarly journals Software Toolchain for Large-Scale RE-NFA Construction on FPGA

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Yi-Hua E. Yang ◽  
Viktor K. Prasanna
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Regular Expression ◽  
Finite Automata ◽  
Fixed Number ◽  
Regular Expressions ◽  
Pattern Complexity ◽  
Regular Expression Matching ◽  
Area Increase ◽  
Prototype Software

We present a software toolchain for constructing large-scaleregular expression matching(REM) on FPGA. The software automates the conversion of regular expressions into compact and high-performance nondeterministic finite automata (RE-NFA). Each RE-NFA is described as an RTL regular expression matching engine (REME) in VHDL for FPGA implementation. Assuming a fixed number of fan-out transitions per state, ann-statem-bytes-per-cycle RE-NFA can be constructed inO(n×m)time andO(n×m)memory by our software. A large number of RE-NFAs are placed onto a two-dimensionalstaged pipeline, allowing scalability to thousands of RE-NFAs with linear area increase and little clock rate penalty due to scaling. On a PC with a 2 GHz Athlon64 processor and 2 GB memory, our prototype software constructs hundreds of RE-NFAs used by Snort in less than 10 seconds. We also designed a benchmark generator which can produce RE-NFAs with configurable pattern complexity parameters, including state count, state fan-in, loop-back and feed-forward distances. Several regular expressions with various complexities are used to test the performance of our RE-NFA construction software.

Expressive capacity of subregular expressions

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 201-218 ◽  
Author(s):  
Martin Kutrib ◽  
Matthias Wendlandt
Keyword(s):  
Regular Languages ◽  
Regular Expressions ◽  
Different Types ◽  
Finite Set ◽  
Unary Languages

Different types of subregular expressions are studied. Each type is obtained by either omitting one of the regular operations or replacing it by complementation or intersection. For uniformity and in order to allow non-trivial languages to be expressed, the set of literals is a finite set of words instead of letters. The power and limitations as well as relations with each other are considered, which is often done in terms of unary languages. Characterizations of some of the language families are obtained. A finite hierarchy is shown that reveals that the operation complementation is generally stronger than intersection. Furthermore, we investigate the closures of language families described by regular expressions with omitted operation under that operation. While it is known that in case of union this closure captures all regular languages, for the cases of concatenation and star incomparability results are obtained with the corresponding language families where the operation is replaced by complementation.

scholarly journals Deterministic automata for extended regular expressions

2017 ◽  
Vol 7 (1) ◽  
pp. 24-28
Author(s):  
Mirzakhmet Syzdykov
Keyword(s):  
Finite Automaton ◽  
Regular Languages ◽  
Regular Expressions ◽  
Deterministic Finite Automaton ◽  
Past Work ◽  
The Past ◽  
Deterministic Automata ◽  
Extended Regular Expressions

Abstract In this work we present the algorithms to produce deterministic finite automaton (DFA) for extended operators in regular expressions like intersection, subtraction and complement. The method like “overriding” of the source NFA(NFA not defined) with subset construction rules is used. The past work described only the algorithm for AND-operator (or intersection of regular languages); in this paper the construction for the MINUS-operator (and complement) is shown.

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