scholarly journals A Class of 2-Head Finite Automata for Linear Languages

Triangle ◽  
2018 ◽  
pp. 89
Author(s):  
Benedek Nagy
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
State Machines ◽  
Deterministic Automata ◽  
Even Linear Languages

Both deterministic and non-deterministic nite state machines (automata) recognize regular languages exactly. Now we extend these machines using two heads to characterize even-linear and linear languages. The heads move in opposite directions in these automata. For even-linear languages, deterministic automata have the same eciency as non-deterministic ones, but for the general case (linear languages) only the non-deterministic version is sucient. We compare our automata to other two-head automata as well.

scholarly journals Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

2017 ◽  
Author(s):  
Theodore Andronikos ◽  
Alla Sirokofskich ◽  
Kalliopi Kastampolidou ◽  
Magdalini Varvouzou ◽  
Konstantinos Giannakis ◽  
...  
Keyword(s):  
Game Theory ◽  
Quantum Computation ◽  
Finite Automata ◽  
State Machines ◽  
Quantum Game ◽  
Finite Games ◽  
New Concepts ◽  
Finite Game ◽  
Finite State ◽  
Deterministic Automata

The meticulous study of finite automata has produced many important and useful results. Automata are simple yet efficient finite state machines that can be utilized in a plethora of situations. It comes, therefore, as no surprise that they have been used in classic game theory in order to model players and their actions. Game theory has recently been influenced by ideas from the field of quantum computation. As a result, quantum versions of classic games have already been introduced and studied. The PQ penny flip game is a famous quantum game introduced by Meyer in 1999. In this paper we investigate all possible finite games that can be played between the two players Q and Picard of the original PQ game. For this purpose we establish a rigorous connection between finite automata and the PQ game along with all its possible variations. Starting from the automaton that corresponds to the original game, we construct more elaborate automata for certain extensions of the game, before finally presenting a semiautomaton that captures the intrinsic behavior of all possible variants of the PQ game. What this means is that from the semiautomaton in question, by setting appropriate initial and accepting states, one can construct deterministic automata able to capture every possible finite game that can be played between the two players Q and Picard. Moreover, we introduce the new concepts of a winning automaton and complete automaton for either player.

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].

Non-Self-Embedding Grammars and Descriptional Complexity

2021 ◽  
Vol 180 (1-2) ◽  
pp. 103-122
Author(s):  
Giovanni Pighizzini ◽  
Luca Prigioniero
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Nondeterministic Automaton ◽  
Deterministic Automaton ◽  
Double Exponential ◽  
Optimal Bounds ◽  
Deterministic Automata ◽  
The Cost ◽  
Context Free ◽  
Exponential Size

Non-self-embedding grammars are a subclass of context-free grammars which only generate regular languages. The size costs of the conversion of non-self-embedding grammars into equivalent finite automata are studied, by proving optimal bounds for the number of states of nondeterministic and deterministic automata equivalent to given non-self-embedding grammars. In particular, each non-self-embedding grammar of size s can be converted into an equivalent nondeterministic automaton which has an exponential size in s and into an equivalent deterministic automaton which has a double exponential size in s. These costs are shown to be optimal. Moreover, they do not change if the larger class of quasi-non-self-embedding grammars, which still generate only regular languages, is considered. In the case of letter bounded languages, the cost of the conversion of non-self-embedding grammars and quasi-non-self-embedding grammars into deterministic automata reduces to an exponential of a polynomial in s.

Finite-State Technology

2018 ◽  
Author(s):  
Mans Hulden
Keyword(s):  
Natural Language Processing ◽  
Natural Language ◽  
Computational Linguistics ◽  
Language Processing ◽  
Finite State Machines ◽  
Regular Languages ◽  
Finite State Automata ◽  
State Machines ◽  
Computational Phonology ◽  
Finite State

Finite-state machines—automata and transducers—are ubiquitous in natural-language processing and computational linguistics. This chapter introduces the fundamentals of finite-state automata and transducers, both probabilistic and non-probabilistic, illustrating the technology with example applications and common usage. It also covers the construction of transducers, which correspond to regular relations, and automata, which correspond to regular languages. The technologies introduced are widely employed in natural language processing, computational phonology and morphology in particular, and this is illustrated through common practical use cases.

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.

General Fuzzy Finite Switchboard Automata

2019 ◽  
Vol 15 (02) ◽  
pp. 283-305 ◽  
Author(s):  
J. Kavikumar ◽  
S. P. Tiwari ◽  
Nur Ain Ebas ◽  
A. H. Nor Shamsidah
Keyword(s):  
Finite Automata ◽  
State Machines ◽  
Fuzzy Topology ◽  
Strongly Connected ◽  
Fuzzy Automata ◽  
General Fuzzy Automata ◽  
Switching State

The constructions of finite switchboard state automata are known to be an extension of finite automata in the view of commutative and switching state machines. This research incorporated an idea of a switchboard in the general fuzzy automata to introduce general fuzzy finite switchboard automata. The attained output reveals that a strongly connected general fuzzy finite switchboard automaton is equivalent to the retrievable general fuzzy automata. Further, the notion of the switchboard subsystem and strong switchboard subsystem of general fuzzy finite switchboard automata are examined. Finally, the concept of fuzzy topology on general fuzzy finite switchboard automata in terms of these characterisations is formulated.

Descriptional Complexity of the Forever Operator

2019 ◽  
Vol 30 (01) ◽  
pp. 115-134 ◽  
Author(s):  
Michal Hospodár ◽  
Galina Jirásková ◽  
Peter Mlynárčik
Keyword(s):  
Regular Language ◽  
Finite Automata ◽  
Deterministic Finite Automata ◽  
State Complexity ◽  
Descriptional Complexity ◽  
Trade Offs ◽  
Number Formula ◽  
Deterministic Automata ◽  
Initial States ◽  
Nondeterministic State

We examine the descriptional complexity of the forever operator, which assigns the language [Formula: see text] to a regular language [Formula: see text], and we investigate the trade-offs between various models of finite automata. We consider complete and partial deterministic finite automata, nondeterministic finite automata with single or multiple initial states, alternating, and Boolean finite automata. We assume that the argument and the result of this operation are accepted by automata belonging to one of these six models. We investigate all possible trade-offs and provide a tight upper bound for 32 of 36 of them. The most interesting result is the trade-off from nondeterministic to deterministic automata given by the Dedekind number [Formula: see text]. We also prove that the nondeterministic state complexity of [Formula: see text] is [Formula: see text] which solves an open problem stated by Birget [The state complexity of [Formula: see text] and its connection with temporal logic, Inform. Process. Lett. 58 (1996) 185–188].

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.

Concise representations of regular languages by degree and probabilistic finite automata

1993 ◽  
Vol 26 (4) ◽  
pp. 379-395 ◽  
Author(s):  
Chandra M. R. Kintala ◽  
Kong -Yee Pun ◽  
Detlef Wotschke
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Probabilistic Finite Automata

scholarly journals The genus of regular languages

2016 ◽  
Vol 28 (1) ◽  
pp. 14-44 ◽  
Author(s):  
GUILLAUME BONFANTE ◽  
FLORIAN DELOUP
Keyword(s):  
Lower Bounds ◽  
Regular Languages ◽  
Upper And Lower Bounds ◽  
Generic Condition ◽  
Finite State ◽  
Large Genus ◽  
Deterministic Automata

The paper defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, an FSA can be seen as a graph for which the notion of genus arises. At the same time, an FSA has a semantics via its underlying language. It is then natural to make a connection between the languages and the notion of genus. After we introduce and justify the the notion of the genus for regular languages, the following questions are addressed. First, depending on the size of the alphabet, we provide upper and lower bounds on the genus of regular languages: we show that under a relatively generic condition on the alphabet and the geometry of the automata, the genus grows at least linearly in terms of the size of the automata. Second, we show that the topological cost of the powerset determinization procedure is exponential. Third, we prove that the notion of minimization is orthogonal to the notion of genus. Fourth, we build regular languages of arbitrary large genus: the notion of genus defines a proper hierarchy of regular languages.

Sign in / Sign up

Export Citation Format

Share Document