Watson–Crick Jumping Finite Automata: Combination, Comparison and Closure

2021 ◽  
Author(s):  
U K Mishra ◽  
K Mahalingam ◽  
R Rama
Keyword(s):  
Finite Automata ◽  
Closure Properties ◽  
Computing Power ◽  
New Model ◽  
Model Of Computation ◽  
Chomsky Hierarchy ◽  
Restricted Version ◽  
State 1

Abstract A new model of computation called Watson–Crick jumping finite automata was introduced by Mahalingam et al., and the authors study the computing power and closure properties of the variants of the model. There are four variants of the model: no state, 1-limited, all-final and simple Watson–Crick jumping finite automata. In this paper, we introduce a restricted version that is a combination of variants of the existing model. It becomes essential to explore the computing power and closure properties of these combinations. The combination variants are extensively compared with Chomsky hierarchy, general jumping finite automata family and among themselves. We also explore the closure properties of such restricted automata.

Watson–Crick Jumping Finite Automata

2020 ◽  
Vol 31 (07) ◽  
pp. 891-913
Author(s):  
Kalpana Mahalingam ◽  
Ujjwal Kumar Mishra ◽  
Rama Raghavan
Keyword(s):  
Finite Automata ◽  
Closure Property ◽  
Closure Properties ◽  
Chomsky Hierarchy ◽  
Language Classes

Watson–Crick jumping finite automata work on tapes which are double stranded sequences of symbols similar to that of Watson–Crick automata. The double stranded sequence is scanned in a discontinuous manner. That is, after reading a double stranded string, the automata can jump over some subsequence and continue scanning depending on the rule. Some variants of such automata are 1-limited, No state, All final and Simple Watson–Crick jumping finite automata. The comparison of the languages accepted by these variants with the language classes in Chomsky hierarchy has been carried out. We investigate some closure properties. We also try to place the duplication closure of a word in Watson–Crick jumping finite automata family. We have discussed the closure property of Watson–Crick jumping finite automata family under duplication operations.

RESTARTING TILING AUTOMATA

2013 ◽  
Vol 24 (06) ◽  
pp. 863-878 ◽  
Author(s):  
DANIEL PRŮŠA ◽  
FRANTIŠEK MRÁZ
Keyword(s):  
Regular Languages ◽  
Two Dimensional ◽  
Scanning Strategy ◽  
Closure Properties ◽  
Computing Device ◽  
New Model ◽  
Picture Languages

We present a new model of a two-dimensional computing device called restarting tiling automaton. The automaton defines a set of tile-rewriting, weight-reducing rules and a scanning strategy by which a tile to rewrite is being searched. We investigate properties of the induced families of picture languages. Special attention is paid to picture languages that can be accepted independently of the scanning strategy. We show that this family strictly includes REC and exhibits similar closure properties. Moreover, we prove that its intersection with the set of one-row languages coincides with the regular languages.

Finite Automata Over Infinite Alphabets: Two Models with Transitions for Local Change

2018 ◽  
Vol 29 (02) ◽  
pp. 213-231
Author(s):  
Christopher Czyba ◽  
Wolfgang Thomas ◽  
Christopher Spinrath
Keyword(s):  
Finite Automata ◽  
Local Change ◽  
Closure Properties ◽  
Open Issues

Two models of automata over infinite alphabets are presented, mainly with a focus on the alphabet [Formula: see text]. In the first model, transitions can refer to logic formulas that connect properties of successive letters. In the second, the letters are considered as columns of a labeled grid which an automaton traverses column by column. Thus, both models focus on the comparison of successive letters, i.e. “local changes”. We prove closure (and non-closure) properties, show the decidability of the respective non-emptiness problems, prove limits on decidability results for extended models, and discuss open issues in the development of a generalized theory.

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

GROUPS WITH INDEXED CO-WORD PROBLEM

2006 ◽  
Vol 16 (05) ◽  
pp. 985-1014 ◽  
Author(s):  
DEREK F. HOLT ◽  
CLAAS E. RÖVER
Keyword(s):  
Dynamical Systems ◽  
Large Class ◽  
Word Problem ◽  
Word Problems ◽  
Automorphism Groups ◽  
Finite Automata ◽  
Restricted Class ◽  
Closure Properties ◽  
Free Products ◽  
Thompson Groups

We investigate co-indexed groups, that is groups whose co-word problem (all words defining nontrivial elements) is an indexed language. We show that all Higman–Thompson groups and a large class of tree automorphism groups defined by finite automata are co-indexed groups. The latter class is closely related to dynamical systems and includes the Grigorchuk 2-group and the Gupta–Sidki 3-group. The co-word problems of all these examples are in fact accepted by nested stack automata with certain additional properties, and we establish various closure properties of this restricted class of co-indexed groups, including closure under free products.

scholarly journals Languages recognized by nondeterministic quantum finite automata

2010 ◽  
Vol 10 (9&10) ◽  
pp. 747-770
Author(s):  
Abuzer Yakaryilmaz ◽  
A.C. Cem Say
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Space Complexity ◽  
Complexity Classes ◽  
Language Recognition ◽  
Closure Properties ◽  
Quantum Finite Automata ◽  
Sublogarithmic Space

The nondeterministic quantum finite automaton (NQFA) is the only known case where a one-way quantum finite automaton (QFA) model has been shown to be strictly superior in terms of language recognition power to its probabilistic counterpart. We give a characterization of the class of languages recognized by NQFAs, demonstrating that it is equal to the class of exclusive stochastic languages. We also characterize the class of languages that are recognized necessarily by two-sided error by QFAs. It is shown that these classes remain the same when the QFAs used in their definitions are replaced by several different model variants that have appeared in the literature. We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.

Quantum Automata with Open Time Evolution

2012 ◽  
pp. 74-89
Author(s):  
Mika Hirvensalo
Keyword(s):  
Time Evolution ◽  
Finite Automaton ◽  
Finite Automata ◽  
Quantum Evolution ◽  
Closure Properties ◽  
Probabilistic Measure ◽  
Quantum Automata ◽  
Open Quantum ◽  
Quantum Measure ◽  
Open Time

In this paper, a model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum automata can be simulated by the open quantum evolution automata without increasing the number of the states.

scholarly journals Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

2015 ◽  
Vol 373 (2046) ◽  
pp. 20140223 ◽  
Author(s):  
Chrystopher L. Nehaniv ◽  
John Rhodes ◽  
Attila Egri-Nagy ◽  
Paolo Dini ◽  
Eric Rothstein Morris ◽  
...  
Keyword(s):  
Systems Biology ◽  
Genetic Regulation ◽  
Krebs Cycle ◽  
Internal Symmetry ◽  
Discrete Models ◽  
Lac Operon ◽  
New Model ◽  
Model Of Computation ◽  
Natural Systems ◽  
Wide Range

Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53–mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to ‘pools of reversibility’. These natural subsystems are related to one another in a hierarchical manner by the notion of ‘ weak control ’. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation . This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.

UNWEIGHTED AND WEIGHTED HYPER-MINIMIZATION

2012 ◽  
Vol 23 (06) ◽  
pp. 1207-1225 ◽  
Author(s):  
ANDREAS MALETTI ◽  
DANIEL QUERNHEIM
Keyword(s):  
Finite Automata ◽  
Reduction Technique ◽  
Regular Languages ◽  
Minimization Algorithm ◽  
Compression Method ◽  
Closure Properties ◽  
State Reduction ◽  
Deterministic Finite Automata ◽  
Input Strings ◽  
Weighted Finite Automata

Hyper-minimization of deterministic finite automata (DFA) is a recently introduced state reduction technique that allows a finite change in the recognized language. A generalization of this lossy compression method to the weighted setting over semifields is presented, which allows the recognized weighted language to differ for finitely many input strings. First, the structure of hyper-minimal deterministic weighted finite automata is characterized in a similar way as in classical weighted minimization and unweighted hyper-minimization. Second, an efficient hyper-minimization algorithm, which runs in time [Formula: see text], is derived from this characterization. Third, the closure properties of canonical regular languages, which are languages recognized by hyper-minimal DFA, are investigated. Finally, some recent results in the area of hyper-minimization are recalled.

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