Boosting Reversible Pushdown and Queue Machines by Preprocessing

2020 ◽  
pp. 1-29
Author(s):  
Holger Bock Axelsen ◽  
Martin Kutrib ◽  
Andreas Malcher ◽  
Matthias Wendlandt
Keyword(s):  
Real Time ◽  
Finite Automata ◽  
Point Of View ◽  
Regular Languages ◽  
Theoretical Point ◽  
Computational Power ◽  
Finite State ◽  
Finite State Transducer ◽  
Context Free ◽  
Pushdown Automata

It is well known that reversible finite automata do not accept all regular languages, that reversible pushdown automata do not accept all deterministic context-free languages, and that reversible queue automata are less powerful than deterministic real-time queue automata. It is of significant interest from both a practical and theoretical point of view to close these gaps. We here extend these reversible models by a preprocessing unit which is basically a reversible injective and length-preserving finite state transducer. It turns out that preprocessing the input using such weak devices increases the computational power of reversible deterministic finite automata to the acceptance of all regular languages, whereas for reversible pushdown automata the accepted family of languages lies strictly in between the reversible deterministic context-free languages and the real-time deterministic context-free languages. For reversible queue automata the preprocessing of the input leads to machines that are stronger than real-time reversible queue automata, but less powerful than real-time deterministic (irreversible) queue automata. Moreover, it is shown that the computational power of all three types of machines is not changed by allowing the preprocessing finite state transducer to work irreversibly. Finally, we examine the closure properties of the family of languages accepted by such machines.

scholarly journals DETERMINISTIC PUSHDOWN AUTOMATA AND UNARY LANGUAGES

2009 ◽  
Vol 20 (04) ◽  
pp. 629-645 ◽  
Author(s):  
GIOVANNI PIGHIZZINI
Keyword(s):  
Finite Automata ◽  
Point Of View ◽  
Deterministic Finite Automaton ◽  
Pushdown Automaton ◽  
Nondeterministic Automaton ◽  
Letter Alphabet ◽  
Finite State ◽  
Unary Languages ◽  
Context Free ◽  
Pushdown Automata

The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, its cost cannot be reduced even if it is performed by a two-way nondeterministic automaton. We also prove that there are unary languages for which deterministic pushdown automata cannot be exponentially more succinct than finite automata. In order to state this result, we investigate the conversion of deterministic pushdown automata into context-free grammars. We prove that in the unary case the number of variables in the resulting grammar is strictly smaller than the number of variables needed in the case of nonunary alphabets.

scholarly journals Reversible parallel communicating finite automata systems

2021 ◽  
Vol 58 (4) ◽  
pp. 263-279
Author(s):  
Henning Bordihn ◽  
György Vaszil
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
The Other ◽  
Deterministic Case ◽  
Computational Power ◽  
Deterministic Finite Automata ◽  
Relationship Of ◽  
The Relationship ◽  
Context Free

AbstractWe study the concept of reversibility in connection with parallel communicating systems of finite automata (PCFA in short). We define the notion of reversibility in the case of PCFA (also covering the non-deterministic case) and discuss the relationship of the reversibility of the systems and the reversibility of its components. We show that a system can be reversible with non-reversible components, and the other way around, the reversibility of the components does not necessarily imply the reversibility of the system as a whole. We also investigate the computational power of deterministic centralized reversible PCFA. We show that these very simple types of PCFA (returning or non-returning) can recognize regular languages which cannot be accepted by reversible (deterministic) finite automata, and that they can even accept languages that are not context-free. We also separate the deterministic and non-deterministic variants in the case of systems with non-returning communication. We show that there are languages accepted by non-deterministic centralized PCFA, which cannot be recognized by any deterministic variant of the same type.

Non-Self-Embedding Grammars, Constant-Height Pushdown Automata, and Limited Automata

2020 ◽  
pp. 1-25
Author(s):  
Bruno Guillon ◽  
Giovanni Pighizzini ◽  
Luca Prigioniero
Keyword(s):  
Finite Automata ◽  
Regular Languages ◽  
Deterministic Finite Automata ◽  
Polynomial Size ◽  
Constant Height ◽  
Double Exponential ◽  
Recursive Structures ◽  
Deterministic Formula ◽  
Context Free ◽  
Pushdown Automata

Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and [Formula: see text]-limited automata to deterministic finite automata. Constant-height pushdown automata and [Formula: see text]-limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size. Furthermore, a polynomial size simulation by [Formula: see text]-limited automata is presented. However, the converse transformation is proved to cost exponential. Finally, a different simulation shows that also the conversion of deterministic constant-height pushdown automata into deterministic [Formula: see text]-limited automata costs polynomial.

scholarly journals One-Time Nondeterministic Computations

2019 ◽  
Vol 30 (06n07) ◽  
pp. 1069-1089
Author(s):  
Markus Holzer ◽  
Martin Kutrib
Keyword(s):  
Finite Automata ◽  
State Machines ◽  
Computational Power ◽  
Deterministic Finite Automaton ◽  
Worst Case ◽  
Trade Offs ◽  
Finite State ◽  
Nondeterministic State ◽  
Pushdown Automata ◽  
Limited Nondeterminism

We introduce the concept of one-time nondeterminism as a new kind of limited nondeterminism for finite state machines and pushdown automata. Roughly speaking, one-time nondeterminism means that at the outset the computation is nondeterministic, but whenever it performs a guess, this guess is fixed for the rest of the computation. We characterize the computational power of one-time nondeterministic finite automata (OTNFAs) and one-time nondeterministic pushdown devices. Moreover, we study the descriptional complexity of these machines. For instance, we show that for an [Formula: see text]-state OTNFA with a sole nondeterministic state, that is nondeterministic for only one input symbol, [Formula: see text] states are sufficient and necessary in the worst case for an equivalent deterministic finite automaton. In case of pushdown automata, the conversion of a nondeterministic to a one-time nondeterministic as well as the conversion of a one-time nondeterministic to a deterministic one turn out to be non-recursive, that is, the trade-offs in size cannot be bounded by any recursive function.

A novel cryptosystem based on abstract automata and Latin cubes

2015 ◽  
Vol 52 (2) ◽  
pp. 221-232
Author(s):  
Pál Dömösi ◽  
Géza Horváth
Keyword(s):  
Block Cipher ◽  
Finite Automata ◽  
Theoretical Background ◽  
Point Of View ◽  
Theoretical Point ◽  
Transition Matrices ◽  
Encryption And Decryption ◽  
Secret Keys ◽  
Automata Network ◽  
Fully Functioning

In this paper we introduce a novel block cipher based on the composition of abstract finite automata and Latin cubes. For information encryption and decryption the apparatus uses the same secret keys, which consist of key-automata based on composition of abstract finite automata such that the transition matrices of the component automata form Latin cubes. The aim of the paper is to show the essence of our algorithms not only for specialists working in compositions of abstract automata but also for all researchers interested in cryptosystems. Therefore, automata theoretical background of our results is not emphasized. The introduced cryptosystem is important also from a theoretical point of view, because it is the first fully functioning block cipher based on automata network.

BORDERS AND FINITE AUTOMATA

2007 ◽  
Vol 18 (04) ◽  
pp. 859-871
Author(s):  
MARTIN ŠIMŮNEK ◽  
BOŘIVOJ MELICHAR
Keyword(s):  
Pattern Matching ◽  
Hamming Distance ◽  
Finite Automata ◽  
Music Analysis ◽  
Theoretical Description ◽  
Specific Form ◽  
Distance Measures ◽  
Computer Assisted ◽  
Finite State ◽  
Finite State Transducer

A border of a string is a prefix of the string that is simultaneously its suffix. It is one of the basic stringology keystones used as a part of many algorithms in pattern matching, molecular biology, computer-assisted music analysis and others. The paper offers the automata-theoretical description of Iliopoulos's ALL_BORDERS algorithm. The algorithm finds all borders of a string with don't care symbols. We show that ALL_BORDERS algorithm is an implementation of a finite state transducer of specific form. We describe how such a transducer can be constructed and what should be the input string like. The described transducer finds a set of lengths of all borders. Last but not least, we define approximate borders and show how to find all approximate borders of a string when we concern Hamming distance definition. Our solution of this problem is based on transducers again. This allows us to use analogy with automata-based pattern matching methods. Finally we discuss conditions under which the same principle can be used for other distance measures.

LIMITED AUTOMATA AND REGULAR LANGUAGES

2014 ◽  
Vol 25 (07) ◽  
pp. 897-916 ◽  
Author(s):  
GIOVANNI PIGHIZZINI ◽  
ANDREA PISONI
Keyword(s):  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Finite State Automata ◽  
Turing Machines ◽  
Double Exponential ◽  
Finite State ◽  
A Cell ◽  
Fixed Constant ◽  
The One ◽  
Context Free

Limited automata are one-tape Turing machines that are allowed to rewrite the content of any tape cell only in the first d visits, for a fixed constant d. In the case d = 1, namely, when a rewriting is possible only during the first visit to a cell, these models have the same power of finite state automata. We prove state upper and lower bounds for the conversion of 1-limited automata into finite state automata. In particular, we prove a double exponential state gap between nondeterministic 1-limited automata and one-way deterministic finite automata. The gap reduces to a single exponential in the case of deterministic 1-limited automata. This also implies an exponential state gap between nondeterministic and deterministic 1-limited automata. Another consequence is that 1-limited automata can have less states than equivalent two-way nondeterministic finite automata. We show that this is true even if we restrict to the case of the one-letter input alphabet. For each d ≥ 2, d-limited automata are known to characterize the class of context-free languages. Using the Chomsky-Schützenberger representation for contextfree languages, we present a new conversion from context-free languages into 2-limited automata.

scholarly journals QUANTUM COUNTER AUTOMATA

2012 ◽  
Vol 23 (05) ◽  
pp. 1099-1116 ◽  
Author(s):  
A. C. CEM SAY ◽  
ABUZER YAKARYILMAZ
Keyword(s):  
Real Time ◽  
Finite Automata ◽  
Affirmative Answer ◽  
Quantum Model ◽  
Open Problems ◽  
Modern Approach ◽  
Context Free Language ◽  
Definition Of ◽  
Context Free ◽  
Free Language

The question of whether quantum real-time one-counter automata (rtQ1CAs) can outperform their probabilistic counterparts has been open for more than a decade. We provide an affirmative answer to this question, by demonstrating a non-context-free language that can be recognized with perfect soundness by a rtQ1CA. This is the first demonstration of the superiority of a quantum model to the corresponding classical one in the real-time case with an error bound less than 1. We also introduce a generalization of the rtQ1CA, the quantum one-way one-counter automaton (1Q1CA), and show that they too are superior to the corresponding family of probabilistic machines. For this purpose, we provide general definitions of these models that reflect the modern approach to the definition of quantum finite automata, and point out some problems with previous results. We identify several remaining open problems.

Investigations on Automata and Languages Over a Unary Alphabet

2015 ◽  
Vol 26 (07) ◽  
pp. 827-850 ◽  
Author(s):  
Giovanni Pighizzini
Keyword(s):  
Computational Models ◽  
The State ◽  
Space Complexity ◽  
Finite State Automata ◽  
Probabilistic Automata ◽  
Letter Alphabet ◽  
Finite State ◽  
Context Free ◽  
Pushdown Automata

The investigation of automata and languages defined over a one letter alphabet shows interesting differences with respect to the case of alphabets with at least two letters. Probably, the oldest example emphasizing one of these differences is the collapse of the classes of regular and context-free languages in the unary case (Ginsburg and Rice, 1962). Many differences have been proved concerning the state costs of the simulations between different variants of unary finite state automata (Chrobak, 1986, Mereghetti and Pighizzini, 2001). We present an overview of these results. Because important connections with fundamental questions in space complexity, we give emphasis to unary two-way automata. Furthermore, we discuss unary versions of other computational models, as probabilistic automata, one-way and two-way pushdown automata, even extended with auxiliary workspace, and multi-head automata.

EFFICIENT DETECTORS AND CONSTRUCTORS FOR SIMPLE LANGUAGES

1991 ◽  
Vol 02 (03) ◽  
pp. 183-205 ◽  
Author(s):  
Dung T. Huynh
Keyword(s):  
Finite Automata ◽  
Boolean Circuits ◽  
Turing Machines ◽  
Constant Depth ◽  
Pushdown Automaton ◽  
Polynomial Size ◽  
Regular Sets ◽  
Context Free ◽  
Pushdown Automata ◽  
Nondeterministic Logspace

In this paper, we investigate the complexity of computing the detector, constructor and lexicographic constructor functions for a given language. The following classes of languages will be considered: (1) context-free languages, (2) regular sets, (3) languages accepted by one-way nondeterministic auxiliary pushdown automata, (4) languages accepted by one-way nondeterministic logspace-bounded Turing machines, (5) two-way deterministic pushdown automaton languages, (6) languages accepted by uniform families of constant-depth polynomial-size Boolean circuits, and (7) languages accepted by multihead finite automata. We show that for the classes (1)–(4), efficient detectors, constructors and lexicographic constructors exist, whereas for (5)– (7) polynomial-time computable detectors, constructors and lexicographic constructors exist iff there are no sparse sets in NP−P (or equivalently, E=NE). Our results provide sharp boundaries between classes of languages which have efficient detectors, constructors and classes of languages for which efficient detectors and constructors do not appear to exist.

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