scholarly journals On deterministic 1-limited 5′ → 3′ sensing Watson–Crick finite-state transducers

2021 ◽  
Vol 55 ◽  
pp. 5
Author(s):  
Benedek Nagy ◽  
Zita Kovács
Keyword(s):  
Dna Computing ◽  
Finite Automata ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Double Stranded Dna ◽  
Finite State Transducers ◽  
Special Cases ◽  
Finite State ◽  
Dna Strands ◽  
Processing Order

Finite automata and finite state transducers belong to the bases of (theoretical) computer science with many applications. On the other hand, DNA computing and related bio-inspired paradigms are relatively new fields of computing. Watson–Crick automata are in the intersection of the above fields. These finite automata have two reading heads as they read the upper and lower strands of the input DNA molecule, respectively. In 5′ → 3′ Watson–Crick automata the two reading heads move in the same biochemical direction, that is, from the 5′ end of the strand to the direction of the 3′ end. However, in the double-stranded DNA, the DNA strands are directed in opposite way to each other, therefore 5′ → 3′ Watson–Crick automata read the input from the two extremes. In sensing 5′ → 3′ automata the automata sense if the two heads are at the same position, moreover, the computing process is finished at that time. Based on this class of automata, we define WK transducers such that, at each transition, exactly one input letter is being processed, and exactly one output letter is written on a normal output tape. Some special cases are defined and analyzed, e.g., when only one of the reading heads is being used and when the transducer has only one state. We also show that the minimal transducer is uniquely defined if the transducer is deterministic and it has marked output, i.e., the output letter written in a step identifies the reading head that is used in that transition. We have also used the functions ‘processing order’ and ‘reading heads’ to analyze these transducers.

GENERAL ALGORITHMS FOR TESTING THE AMBIGUITY OF FINITE AUTOMATA AND THE DOUBLE-TAPE AMBIGUITY OF FINITE-STATE TRANSDUCERS

2011 ◽  
Vol 22 (04) ◽  
pp. 883-904 ◽  
Author(s):  
CYRIL ALLAUZEN ◽  
MEHRYAR MOHRI ◽  
ASHISH RASTOGI
Keyword(s):  
General Problem ◽  
Finite Automata ◽  
General Algorithm ◽  
Approximate Computation ◽  
Probabilistic Automaton ◽  
Bounded Delay ◽  
Finite State Transducers ◽  
Specific Analysis ◽  
Finite State

We present efficient algorithms for testing the finite, polynomial, and exponential ambiguity of finite automata with ε-transitions. We give an algorithm for testing the exponential ambiguity of an automaton A in time [Formula: see text], and finite or polynomial ambiguity in time [Formula: see text], where |A|E denotes the number of transitions of A. These complexities significantly improve over the previous best complexities given for the same problem. Furthermore, the algorithms presented are simple and based on a general algorithm for the composition or intersection of automata. Additionally, we give an algorithm to determine in time [Formula: see text] the degree of polynomial ambiguity of a polynomially ambiguous automaton A and present an application of our algorithms to an approximate computation of the entropy of a probabilistic automaton. We also study the double-tape ambiguity of finite-state transducers. We show that the general problem is undecidable and that it is NP-hard for acyclic transducers. We present a specific analysis of the double-tape ambiguity of transducers with bounded delay. In particular, we give a characterization of double-tape ambiguity for synchronized transducers with zero delay that can be tested in quadratic time and give an algorithm for testing the double-tape ambiguity of transducers with bounded delay.

Towards a Bio-Inspired Theoretical Linguistics to Model Man-Machine Communication

2013 ◽  
Vol 1 (1) ◽  
pp. 14-28
Author(s):  
Gemma Bel-Enguix ◽  
M. Dolores Jiménez-López
Keyword(s):  
Molecular Biology ◽  
Natural Language ◽  
Computer Science ◽  
Dna Computing ◽  
Membrane Computing ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Theoretical Linguistics ◽  
Machine Communication ◽  
Natural Description

The paper provides an overview of what could be a new biological-inspired linguistics. The authors discuss some reasons for attempting a more natural description of natural language, lying on new theories of molecular biology and their formalization within the area of theoretical computer science. The authors especially explore three bio-inspired models of computation –DNA computing, membrane computing and networks of evolutionary processors (NEPs) – and their possibilities for achieving a simpler, more natural, and mathematically consistent theoretical linguistics.

On the algorithmic complexity of crystals

2014 ◽  
Vol 78 (2) ◽  
pp. 415-435 ◽  
Author(s):  
S. V. Krivovichev
Keyword(s):  
Computer Science ◽  
Coordination Polymers ◽  
Finite Automata ◽  
Theoretical Computer Science ◽  
Algorithmic Complexity ◽  
Inorganic Materials ◽  
Important Class ◽  
Theoretical Computer ◽  
Deterministic Finite Automata ◽  
Orthogonal Networks

AbstractThe concept of the algorithmic complexity of crystals is developed for a particular class of minerals and inorganic materials based on orthogonal networks, which are defined as networks derived from the primitive cubic net (pcu) by the removal of some vertices and/or edges. Orthogonal networks are an important class of networks that dominate topologies of inorganic oxysalts, framework silicates and aluminosilicate minerals, zeolites and coordination polymers. The growth of periodic orthogonal networks may be modelled using structural automata, which are finite automata with states corresponding to vertex configurations and transition symbols corresponding to the edges linking the respective vertices. The model proposed describes possible relations between theoretical crystallography and theoretical computer science through the theory of networks and the theory of deterministic finite automata.

ON THE DISAMBIGUATION OF FINITE AUTOMATA AND FUNCTIONAL TRANSDUCERS

2013 ◽  
Vol 24 (06) ◽  
pp. 847-862 ◽  
Author(s):  
MEHRYAR MOHRI
Keyword(s):  
Finite Automata ◽  
Full Description ◽  
Finite State Transducers ◽  
Finite State ◽  
The One

This paper introduces a new disambiguation algorithm for finite automata and functional finite-state transducers. It gives a full description of this algorithm, including a detailed pseudocode and analysis, and several illustrating examples. The algorithm is often more efficient and the result dramatically smaller than the one obtained using determinization for finite automata or the construction of Schützenberger. The unambiguous automaton or transducer created by our algorithm are never larger than those generated by the construction of Schützenberger. In fact, in a variety of cases, the size of the unambiguous transducer returned by our algorithm is only linear in that of the input transducer while the transducer created by the construction of Schützenberger is exponentially larger. Our algorithm can be used effectively in many applications to make automata and transducers more efficient to use.

scholarly journals Degrees of Infinite Words, Polynomials and Atoms

2018 ◽  
Vol 29 (05) ◽  
pp. 825-843 ◽  
Author(s):  
Jörg Endrullis ◽  
Juhani Karhumäki ◽  
Jan Willem Klop ◽  
Aleksi Saarela
Keyword(s):  
Finite Automata ◽  
Classification Problem ◽  
Turing Degrees ◽  
Turing Machines ◽  
Infinite Words ◽  
Fine Grained ◽  
Finite State Transducers ◽  
Pure Mathematics ◽  
Wide Range ◽  
Finite State

We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite automata for recognising and transforming languages are well-understood, very little is known about the power of automata to transform infinite words. The word transformation realised by finite-state transducers gives rise to a complexity comparison of words and thereby induces equivalence classes, called (transducer) degrees, and a partial order on these degrees. The ensuing hierarchy of degrees is analogous to the recursion-theoretic degrees of unsolvability, also known as Turing degrees, where the transformational devices are Turing machines. However, as a complexity measure, Turing machines are too strong: they trivialise the classification problem by identifying all computable words. Finite-state transducers give rise to a much more fine-grained, discriminating hierarchy. In contrast to Turing degrees, hardly anything is known about transducer degrees, in spite of their naturality. We use methods from linear algebra and analysis to show that there are infinitely many atoms in the transducer degrees, that is, minimal non-trivial degrees.

scholarly journals Non Uniform Random Walks

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Nisheeth Vishnoi
Keyword(s):  
Random Walk ◽  
Theoretical Computer Science ◽  
Expected Number ◽  
Theoretical Computer ◽  
Expected Time ◽  
Special Cases ◽  
Natural Variant ◽  
International Audience ◽  
Parameterized Family ◽  
Open Question

International audience Given $\epsilon _i ∈ [0,1)$ for each $1 < i < n$, a particle performs the following random walk on $\{1,2,...,n\:\}$par If the particle is at $n$, it chooses a point uniformly at random (u.a.r.) from $\{1,...,n-1\}$. If the current position of the particle is $m (1 < m < n)$, with probability $\epsilon _m$ it decides to go back, in which case it chooses a point u.a.r. from $\{m+1,...,n\}$. With probability $1-\epsilon _m$ it decides to go forward, in which case it chooses a point u.a.r. from $\{1,...,m-1\}$. The particle moves to the selected point. What is the expected time taken by the particle to reach 1 if it starts the walk at $n$? Apart from being a natural variant of the classical one dimensional random walk, variants and special cases of this problemarise in Theoretical Computer Science [Linial, Fagin, Karp, Vishnoi]. In this paper we study this problem and observe interesting properties of this walk. First we show that the expected number of times the particle visits $i$ (before getting absorbed at 1) is the same when the walk is started at $j$, for all $j > i$. Then we show that for the following parameterized family of $\epsilon 's: \epsilon _i = \frac{n-i}{n-i+ α · (i-1)}$,$1 < i < n$ where $α$ does not depend on $i$, the expected number of times the particle visits $i$ is the same when the walk is started at $j$, for all $j < i$. Using these observations we obtain the expected absorption time for this family of $\epsilon 's$. As $α$ varies from infinity to 1, this time goes from $Θ (log n) to Θ (n)$. Finally we studythe behavior of the expected convergence timeas a function of $\epsilon$ . It remains an open question to determine whether this quantity increases when all $\epsilon 's$ are increased. We give some preliminary results to this effect.

scholarly journals Automata in SageMath---Combinatorics meet Theoretical Computer Science

2016 ◽  
Vol Vol. 18 no. 3 (Analysis of Algorithms) ◽  
Author(s):  
Clemens Heuberger ◽  
Daniel Krenn ◽  
Sara Kropf
Keyword(s):  
Computer Science ◽  
Finite State Machine ◽  
State Machine ◽  
Combinatorial Problems ◽  
Theoretical Computer Science ◽  
Hamming Weight ◽  
Software System ◽  
Theoretical Computer ◽  
Finite State ◽  
Mathematics Software

The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and transducers and solved using SageMath. In particular, we compute the asymptotic Hamming weight of a non-adjacent-form-like digit expansion, which was not known before.

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