Applications of the finite state automata for counting restricted permutations and variations

In this paper, we use the finite state automata to count the number of restricted permutations and the number of restricted variations. For each type of restricted permutations, we construct a finite state automaton able to recognize and enumerate them. We, also, discuss how it encompasses the other known methods for enumerating permutations with restricted position, and in one case, we establish connections with some other combinatorial structures, such as subsets and compositions.

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Copyful Streaming String Transducers

Fundamenta Informaticae ◽

10.3233/fi-2021-1998 ◽

2021 ◽

Vol 178 (1-2) ◽

pp. 59-76

Author(s):

Emmanuel Filiot ◽

Pierre-Alain Reynier

Keyword(s):

Polynomial Time ◽

Equivalence Problem ◽

Expressive Power ◽

The Other ◽

Finite State Automata ◽

Finite State ◽

Variable Content ◽

Deterministic Automata ◽

Intermediate Output ◽

Linear Manner

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows: (i)HDT0L systems and total deterministic copyful SST have the same expressive power, (ii)the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in quadratic time. As a consequence, equivalence of deterministic SST is decidable, (iii)the functionality of non-deterministic copyful SST is decidable, (iv)determining whether a non-deterministic copyful SST can be transformed into an equivalent non-deterministic copyless SST is decidable in polynomial time.

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Tricolor automata

Proceedings of Balisage: The Markup Conference 2015 ◽

10.4242/balisagevol15.sperberg-mcqueen01 ◽

2015 ◽

Author(s):

C. M. Sperberg-McQueen

Keyword(s):

Regular Languages ◽

The Other ◽

Finite State Automata ◽

Simple Application ◽

Finite State

Tricolor automata are extensions of finite state automata, intended for the comparison of two regular languages; states and arcs in the automaton are colored to indicate whether they are peculiar to one language or the other, or common to both. Their design represents a simple application to practical purposes of ideas derived from the work of Glushkov and Brzozowski. Examples are given to show how tricolor automata can be used to visualize the intersection, union, and set difference of two languages, and algorithms for constructing them are given.

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KNUTH–BENDIX FOR GROUPS WITH INFINITELY MANY RULES

International Journal of Algebra and Computation ◽

10.1142/s0218196700000352 ◽

2000 ◽

Vol 10 (05) ◽

pp. 539-589 ◽

Cited By ~ 1

Author(s):

D. B. A. EPSTEIN ◽

P. J. SANDERS

Keyword(s):

Computer Program ◽

Regular Language ◽

The Body ◽

Finite State Automaton ◽

Finite State Automata ◽

Central Feature ◽

Rapid Reduction ◽

Automatic Structures ◽

Small Constant ◽

Finite State

We introduce a new class of groups with solvable word problem, namely groups specified by a confluent set of short-lex-reducing Knuth–Bendix rules which form a regular language. This simultaneously generalizes short-lex-automatic groups and groups with a finite confluent set of short-lex-reducing rules. We describe a computer program which looks for such a set of rules in an arbitrary finitely presented group. Our main theorem is that our computer program finds the set of rules, if it exists, given enough time and space. (This is an optimistic description of our result — for the more pessimistic details, see the body of the paper.) The set of rules is embodied in a finite state automaton in two variables. A central feature of our program is an operation, which we call welding, used to combine existing rules with new rules as they are found. Welding can be defined on arbitrary finite state automata, and we investigate this operation in abstract, proving that it can be considered as a process which takes as input one regular language and outputs another regular language. In our programs we need to convert several nondeterministic finite state automata to deterministic versions accepting the same language. We show how to improve somewhat on the standard subset construction, due to special features in our case. We axiomatize these special features, in the hope that these improvements can be used in other applications. The Knuth–Bendix process normally spends most of its time in reduction, so its efficiency depends on doing reduction quickly. Standard data structures for doing this can become very large, ultimately limiting the set of presentations of groups which can be so analyzed. We are able to give a method for rapid reduction using our much smaller two variable automaton, encoding the (usually infinite) regular language of rules found so far. Time taken for reduction in a given group is a small constant times the time taken for reduction in the best schemes known (see [5]), which is not too bad since we are reducing with respect to an infinite set of rules, whereas known schemes use a finite set of rules. We hope that the method described here might lead to the computation of automatic structures in groups for which this is currently infeasible. Some proofs have been omitted from this paper in the interests of brevity. Full details are provided in [4].

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Non Homogeneous Rough Finite State Automaton

Revista Gestão Inovação e Tecnologias ◽

10.47059/revistageintec.v11i2.1700 ◽

2021 ◽

Vol 11 (2) ◽

pp. 629-641

Author(s):

B. Praba ◽

R. Saranya

Keyword(s):

Artificial Intelligence ◽

Machine Learning ◽

Dynamical Behaviour ◽

Finite State Automaton ◽

Finite State Automata ◽

Lower Approximation ◽

Upper Approximation ◽

Finite State ◽

Transition Map

Objective: The study of finite state automaton is an essential tool in machine learning and artificial intelligence. The class of rough finite state automaton captures the uncertainty using the rough transition map. The need to generalize this concept arises to adhere the dynamical behaviour of the system. Hence this paper focuses on defining non-homogeneous rough finite state automaton. Methodology: With the aid of Rough finite state automata we define the concept of non-homogeneous rough finite state automata. Findings: Non homogeneous Rough Finite State Automata (NRFSA) Mt is defined by a tuple (Q,Σ,δt,q0 (t),F(t)) The dynamical behaviour of any system can be expressed in terms of an information system at time t. This leads us to define non-homogeneous rough finite state automaton. For each time ‘t’ we generate lower approximation rough finite state automaton Mt_ and the upper approximation rough finite state automaton Mt- and the defined concepts are elaborated with suitable examples. The ordered pair , Mt=(M(t)-,M(t)-) is called as the non-homogeneous rough finite state automaton. Conclusion: Over all our study reveals the characterization of the system which changes its behaviour dynamically over a time ‘t’. Novelty: The novelty of the proposed article is that it clearly immense the system behaviour over a time ‘t’. Using this concept the possible and the definite transitions in the system can be calculated in any given time ‘t’.

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A Transformation-Based Approach to Implication of GSTE Assertion Graphs

Journal of Applied Mathematics ◽

10.1155/2013/709071 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

Guowu Yang ◽

William N. N. Hung ◽

Xiaoyu Song ◽

Wensheng Guo

Keyword(s):

Model Checking ◽

Directed Graphs ◽

Classical Model ◽

Regular Languages ◽

Finite State Automaton ◽

Finite State Automata ◽

Symbolic Trajectory Evaluation ◽

Finite State ◽

Symbolic Trajectory ◽

Language Containment

Generalized symbolic trajectory evaluation (GSTE) is a model checking approach and has successfully demonstrated its powerful capacity in formal verification of VLSI systems. GSTE is an extension of symbolic trajectory evaluation (STE) to the model checking ofω-regular properties. It is an alternative to classical model checking algorithms where properties are specified as finite-state automata. In GSTE, properties are specified as assertion graphs, which are labeled directed graphs where each edge is labeled with two labeling functions: antecedent and consequent. In this paper, we show the complement relation between GSTE assertion graphs and finite-state automata with the expressiveness of regular languages andω-regular languages. We present an algorithm that transforms a GSTE assertion graph to a finite-state automaton and vice versa. By applying this algorithm, we transform the problem of GSTE assertion graphs implication to the problem of automata language containment. We demonstrate our approach with its application to verification of an FIFO circuit.

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Incremental Construction and Maintenance of Minimal Finite-State Automata

Computational Linguistics ◽

10.1162/089120102760173652 ◽

2002 ◽

Vol 28 (2) ◽

pp. 207-216 ◽

Cited By ~ 26

Author(s):

Rafael C. Carrasco ◽

Mikel L. Forcada

Keyword(s):

Computational Linguistics ◽

Efficient Method ◽

Finite State Automaton ◽

Finite State Automata ◽

Construction Problem ◽

Finite State ◽

Single String ◽

Intersection Operation ◽

Incremental Construction ◽

Special Case

Daciuk et al. [Computational Linguistics 26(1):3–16 (2000)] describe a method for constructing incrementally minimal, deterministic, acyclic finite-state automata (dictionaries) from sets of strings. But acyclic finite-state automata have limitations: For instance, if one wants a linguistic application to accept all possible integer numbers or Internet addresses, the corresponding finite-state automaton has to be cyclic. In this article, we describe a simple and equally efficient method for modifying any minimal finite-state automaton (be it acyclic or not) so that a string is added to or removed from the language it accepts; both operations are very important when dictionary maintenance is performed and solve the dictionary construction problem addressed by Daciuk et al. as a special case. The algorithms proposed here may be straightforwardly derived from the customary textbook constructions for the intersection and the complementation of finite-state automata; the algorithms exploit the special properties of the automata resulting from the intersection operation when one of the finite-state automata accepts a single string.

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Comments on “Incremental Construction and Maintenance of Minimal Finite-State Automata,” by Rafael C. Carrasco and Mikel L. Forcada

Computational Linguistics ◽

10.1162/089120104323093302 ◽

2004 ◽

Vol 30 (2) ◽

pp. 227-235 ◽

Cited By ~ 3

Author(s):

Jan Daciuk

Keyword(s):

On the Derivational Entropy of Left-to-Right Probabilistic Finite-State Automata and Hidden Markov Models

Computational Linguistics ◽

10.1162/coli_a_00306 ◽

2018 ◽

Vol 44 (1) ◽

pp. 17-37 ◽

Cited By ~ 1

Author(s):

Joan Andreu Sánchez ◽

Martha Alicia Rocha ◽

Verónica Romero ◽

Mauricio Villegas

Keyword(s):

Hidden Markov Models ◽

Markov Models ◽

Hidden Markov ◽

Finite State Automaton ◽

Finite State Automata ◽

Efficient Computation ◽

Finite State ◽

Probabilistic Finite State Automata ◽

State Models ◽

Finite State Models

Probabilistic finite-state automata are a formalism that is widely used in many problems of automatic speech recognition and natural language processing. Probabilistic finite-state automata are closely related to other finite-state models as weighted finite-state automata, word lattices, and hidden Markov models. Therefore, they share many similar properties and problems. Entropy measures of finite-state models have been investigated in the past in order to study the information capacity of these models. The derivational entropy quantifies the uncertainty that the model has about the probability distribution it represents. The derivational entropy in a finite-state automaton is computed from the probability that is accumulated in all of its individual state sequences. The computation of the entropy from a weighted finite-state automaton requires a normalized model. This article studies an efficient computation of the derivational entropy of left-to-right probabilistic finite-state automata, and it introduces an efficient algorithm for normalizing weighted finite-state automata. The efficient computation of the derivational entropy is also extended to continuous hidden Markov models.

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Functional approach to deterministic finite-state automata systems dynamic modeling

Izvestiya vysshikh uchebnykh zavedenii Gornyi zhurnal ◽

10.21440/0536-1028-2021-2-113-122 ◽

2021 ◽

Vol 1 ◽

pp. 113-122

Author(s):

Eduard S. Lapin ◽

◽

Marat I. Abdrakhmanov ◽

Keyword(s):

Dynamic Modeling ◽

Mining Industry ◽

Good Alternative ◽

Functional Approach ◽

Algorithm Analysis ◽

Substantial Part ◽

Finite State Automaton ◽

Finite State Automata ◽

Advantages And Disadvantages ◽

Finite State

Research aim is to study the functional approach to modeling the deterministic finite-state automata system which is not confined to the elements communication topology and the heterogeneity of the algorithm types. Relevance. The substantial part of engineering systems applied in the mining industry may be described through the finite-state automaton model. They include the mine conveyor systems, shaft signal systems, processing facilities control systems, etc. Such model makes it possible to shorten the time spent on control software development and carry out algorithm analysis, debug, and testing effectively. There are a lot of effective approaches and tools to solve the problem of finite-state automata dynamic modeling, each of which has its own advantages and disadvantages. Methodology. In this article, the methodology of finite-state automata systems modeling is considered as applied to mine conveyor systems. Results. Final-state automata (FSA) models have been developed together with the conditions for FSA systems dynamic modeling as applied to mine conveyor systems. Conclusions. The considered approach to modeling, which involves functors and applicative functors 122 "Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal". No. 2. 2021 ISSN 0536-1028 for structure composition and its operational dynamics study, as well as the possibility to mathematically prove the model’s properties, makes the approach a good alternative when choosing tools for systems models development.

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BERGMAN under MS-DOS and Anick's resolution

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.237 ◽

1997 ◽

Vol Vol. 1 ◽

Author(s):

S. Cojocaru ◽

V. Ufnarovski

Keyword(s):

Hilbert Series ◽

The Other ◽

Finite State Automata ◽

Universal Enveloping Algebras ◽

Generators And Relations ◽

Enveloping Algebras ◽

Finite State ◽

Algorithmic Problems ◽

Noncommutative Algebras ◽

International Audience

International audience Noncommutative algebras, defined by the generators and relations, are considered. The definition and main results connected with the Gröbner basis, Hilbert series and Anick's resolution are formulated. Most attention is paid to universal enveloping algebras. Four main examples illustrate the main concepts and ideas. Algorithmic problems arising in the calculation of the Hilbert series are investigated. The existence of finite state automata, defining thebehaviour of the Hilbert series, is discussed. The extensions of the BERGMAN package for IBM PC compatible computers are described. A table is provided permitting a comparison of the effectiveness of the calculations in BERGMAN with the other systems.

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