Search for a substring of characters using the theory of non-deterministic finite automata and vector-character architecture

The paper proposed an algorithm which purpose is searching for a substring of characters in a string. Principle of its operation is based on the theory of non-deterministic finite automata and vector-character architecture. It is able to provide the linear computational complexity of searching for a substring depending on the length of the searched string measured in the number of operations with hyperdimensional vectors when repeatedly searching for different strings in a target line. None of the existing algorithms has such a low level of computational complexity. The disadvantages of the proposed algorithm are the fact that the existing hardware implementations of computing systems for performing operations with hyperdimensional vectors require a large number of machine instructions, which reduces the gain from this algorithm. Despite this, in the future, it is possible to create a hardware implementation that can ensure the execution of operations with hyperdimensional vectors in one cycle, which will allow the proposed algorithm to be applied in practice.

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FROM EQUIVALENCE TO ALMOST-EQUIVALENCE, AND BEYOND: MINIMIZING AUTOMATA WITH ERRORS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054113400327 ◽

2013 ◽

Vol 24 (07) ◽

pp. 1083-1097 ◽

Cited By ~ 4

Author(s):

MARKUS HOLZER ◽

SEBASTIAN JAKOBI

Keyword(s):

Computational Complexity ◽

Finite Number ◽

Finite Automata ◽

Deterministic Finite Automata ◽

Minimization Problems ◽

Significant Difference ◽

Straightforward Generalization

We introduce E-equivalence, which is a straightforward generalization of almost-equivalence. While almost-equivalence asks for ordinary equivalence up to a finite number of exceptions, in E-equivalence these exceptions or errors must belong to a (regular) set E. The computational complexity of deterministic finite automata (DFAs) minimization problems and their variants w.r.t. almost- and E-equivalence are studied. We show that there is a significant difference in the complexity of problems related to almost-equivalence, and those related to E-equivalence. Moreover, since hyper-minimal and E-minimal automata are not necessarily unique (up to isomorphism as for minimal DFAs), we consider the problem of counting the number of these minimal automata.

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Minimal and Hyper-Minimal Biautomata

International Journal of Foundations of Computer Science ◽

10.1142/s0129054116400050 ◽

2016 ◽

Vol 27 (02) ◽

pp. 161-185

Author(s):

Markus Holzer ◽

Sebastian Jakobi

Keyword(s):

Computational Complexity ◽

Minimization Problem ◽

Finite Automata ◽

Deterministic Finite Automata ◽

Np Complete ◽

Carry Over

We compare deterministic finite automata (DFAs) and biautomata under the following two aspects: structural similarities between minimal and hyper-minimal automata, and computational complexity of the minimization and hyper-minimization problem. Concerning classical minimality, the known results such as isomorphism between minimal DFAs, and NL-completeness of the DFA minimization problem carry over to the biautomaton case. But surprisingly this is not the case for hyper-minimization: the similarity between almost-equivalent hyper-minimal biautomata is not as strong as it is between almost-equivalent hyper-minimal DFAs. Moreover, while hyper-minimization is NL-complete for DFAs, we prove that this problem turns out to be computationally intractable, i.e., NP-complete, for biautomata.

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Brain-Inspired Hardware Solutions for Inference in Bayesian Networks

Frontiers in Neuroscience ◽

10.3389/fnins.2021.728086 ◽

2021 ◽

Vol 15 ◽

Author(s):

Leila Bagheriye ◽

Johan Kwisthout

Keyword(s):

Bayesian Networks ◽

Analog Circuits ◽

Hardware Implementation ◽

Computing Systems ◽

Stochastic Computing ◽

Computing Paradigm ◽

Mixed Signal Circuits ◽

Hardware Implementations ◽

Implementation Problems ◽

Recent Attention

The implementation of inference (i.e., computing posterior probabilities) in Bayesian networks using a conventional computing paradigm turns out to be inefficient in terms of energy, time, and space, due to the substantial resources required by floating-point operations. A departure from conventional computing systems to make use of the high parallelism of Bayesian inference has attracted recent attention, particularly in the hardware implementation of Bayesian networks. These efforts lead to several implementations ranging from digital circuits, mixed-signal circuits, to analog circuits by leveraging new emerging nonvolatile devices. Several stochastic computing architectures using Bayesian stochastic variables have been proposed, from FPGA-like architectures to brain-inspired architectures such as crossbar arrays. This comprehensive review paper discusses different hardware implementations of Bayesian networks considering different devices, circuits, and architectures, as well as a more futuristic overview to solve existing hardware implementation problems.

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NONDETERMINISTIC FINITE AUTOMATA — RECENT RESULTS ON THE DESCRIPTIONAL AND COMPUTATIONAL COMPLEXITY

International Journal of Foundations of Computer Science ◽

10.1142/s0129054109006747 ◽

2009 ◽

Vol 20 (04) ◽

pp. 563-580 ◽

Cited By ~ 26

Author(s):

MARKUS HOLZER ◽

MARTIN KUTRIB

Keyword(s):

Computational Complexity ◽

Finite Automata ◽

Size Estimation ◽

Deterministic Finite Automata ◽

State Complexity ◽

Nondeterministic Finite Automata ◽

Vast Literature ◽

Recent Developments ◽

Big Picture ◽

Main Ideas

Nondeterministic finite automata (NFAs) were introduced in [68], where their equivalence to deterministic finite automata was shown. Over the last 50 years, a vast literature documenting the importance of finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss recent developments relevant to NFAs related problems like, for example, (i) simulation of and by several types of finite automata, (ii) minimization and approximation, (iii) size estimation of minimal NFAs, and (iv) state complexity of language operations. We thus come across descriptional and computational complexity issues of nondeterministic finite automata. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved.

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Two Extensions of Cover Automata

Axioms ◽

10.3390/axioms10040338 ◽

2021 ◽

Vol 10 (4) ◽

pp. 338

Author(s):

Cezar Câmpeanu

Keyword(s):

Computational Complexity ◽

Finite Automata ◽

The State ◽

Finite Cover ◽

Deterministic Finite Automata ◽

State Complexity ◽

Compact Representations ◽

Minimization Algorithms ◽

Deterministic Automata ◽

Representation Transformation

Deterministic Finite Cover Automata (DFCA) are compact representations of finite languages. Deterministic Finite Automata with “do not care” symbols and Multiple Entry Deterministic Finite Automata are both compact representations of regular languages. This paper studies the benefits of combining these representations to get even more compact representations of finite languages. DFCAs are extended by accepting either “do not care” symbols or considering multiple entry DFCAs. We study for each of the two models the existence of the minimization or simplification algorithms and their computational complexity, the state complexity of these representations compared with other representations of the same language, and the bounds for state complexity in case we perform a representation transformation. Minimization for both models proves to be NP-hard. A method is presented to transform minimization algorithms for deterministic automata into simplification algorithms applicable to these extended models. DFCAs with “do not care” symbols prove to have comparable state complexity as Nondeterministic Finite Cover Automata. Furthermore, for multiple entry DFCAs, we can have a tight estimate of the state complexity of the transformation into equivalent DFCA.

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Efficient Construction of the Equation Automaton

Algorithms ◽

10.3390/a14080238 ◽

2021 ◽

Vol 14 (8) ◽

pp. 238

Author(s):

Faissal Ouardi ◽

Zineb Lotfi ◽

Bilal Elghadyry

Keyword(s):

Computational Complexity ◽

Fast Algorithm ◽

Time Complexity ◽

Regular Expression ◽

Finite Automata ◽

Fast Computation ◽

Minimization Algorithm ◽

Deterministic Finite Automata ◽

Efficient Construction ◽

Time And Space Complexity

This paper describes a fast algorithm for constructing directly the equation automaton from the well-known Thompson automaton associated with a regular expression. Allauzen and Mohri have presented a unified construction of small automata and gave a construction of the equation automaton with time and space complexity in O(mlogm+m2), where m denotes the number of Thompson automaton transitions. It is based on two classical automata operations, namely epsilon-removal and Hopcroft’s algorithm for deterministic Finite Automata (DFA) minimization. Using the notion of c-continuation, Ziadi et al. presented a fast computation of the equation automaton in O(m2) time complexity. In this paper, we design an output-sensitive algorithm combining advantages of the previous algorithms and show that its computational complexity can be reduced to O(m×|Q≡e|), where |Q≡e| denotes the number of states of the equation automaton, by an epsilon-removal and Bubenzer minimization algorithm of an Acyclic Deterministic Finite Automata (ADFA).

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