Search results for "Automaton"

Local Normal Forms for First-Order Logic with Applications to Games and Automata

1999

Building on work of Gaifman [Gai82] it is shown that every first-order formula is logically equivalent to a formula of the form ∃ x_1,...,x_l, \forall y, φ where φ is r-local around y, i.e. quantification in φ is restricted to elements of the universe of distance at most r from y. \par From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler, one of the two players. This makes proofs of the existence of a winning strategy for the duplicator, the other player, easier and can thus simplify inexpressibility proofs. \par As another application, automata mode…

Mathematical logic and quantum finite state automata

2009

AbstractThis paper is a review of the connection between formulas of logic and quantum finite-state automata in respect to the language recognition and acceptance probability of quantum finite-state automata. As is well known, logic has had a great impact on classical computation, it is promising to study the relation between quantum finite-state automata and mathematical logic. After a brief introduction to the connection between classical computation and logic, the required background of the logic and quantum finite-state automata is provided and the results of the connection between quantum finite-state automata and logic are presented.

From Nerode's congruence to Suffix Automata with mismatches

2009

AbstractIn this paper we focus on the minimal deterministic finite automaton Sk that recognizes the set of suffixes of a word w up to k errors. As first result we give a characterization of the Nerode’s right-invariant congruence that is associated with Sk. This result generalizes the classical characterization described in [A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M. Chen, J. Seiferas, The smallest automaton recognizing the subwords of a text, Theoretical Computer Science, 40, 1985, 31–55]. As second result we present an algorithm that makes use of Sk to accept in an efficient way the language of all suffixes of w up to k errors in every window of size r of a text, where r is the…

Extending formal language hierarchies to higher dimensions

1999

From Arithmetic to Logic based AI: A Comparative Analysis of Neural Networks and Tsetlin Machine

2020

Neural networks constitute a well-established design method for current and future generations of artificial intelligence. They depends on regressed arithmetic between perceptrons organized in multiple layers to derive a set of weights that can be used for classification or prediction. Over the past few decades, significant progress has been made in low-complexity designs enabled by powerful hardware/software ecosystems. Built on the foundations of finite-state automata and game theory, Tsetlin Machine is increasingly gaining momentum as an emerging artificial intelligence design method. It is fundamentally based on propositional logic based formulation using booleanized input features. Rec…

Solving Stochastic Nonlinear Resource Allocation Problems Using a Hierarchy of Twofold Resource Allocation Automata

2010

In a multitude of real-world situations, resources must be allocated based on incomplete and noisy information. However, in many cases, incomplete and noisy information render traditional resource allocation techniques ineffective. The decentralized Learning Automata Knapsack Game (LAKG) was recently proposed for solving one such class of problems, namely the class of Stochastic Nonlinear Fractional Knapsack Problems. Empirically, the LAKG was shown to yield a superior performance when compared to methods which are based on traditional parameter estimation schemes. This paper presents a completely new online Learning Automata (LA) system, namely the Hierarchy of Twofold Resource Allocation …

Jahn-Teller effect in molecular electronics: quantum cellular automata

2017

The article summarizes the main results of application of the theory of the Jahn-Teller (JT) and pseudo JT effects to the description of molecular quantum dot cellular automata (QCA), a new paradigm of quantum computing. The following issues are discussed: 1) QCA as a new paradigm of quantum computing, principles and advantages; 2) molecular implementation of QCA; 3) role of the JT effect in charge trapping, encoding of binary information in the quantum cell and non-linear cell-cell response; 4) spin-switching in molecular QCA based on mixed-valence cell; 5) intervalence optical absorption in tetrameric molecular mixed-valence cell through the symmetry assisted approach to the multimode/mul…

Representation of Autonomous Automata

2001

An autonomous automaton is a finite automaton with output in which the input alphabet has cardinality one when special reduced. We define the transition from automata to semigroups via a representation successful if given two incomparable automata (neither simulate the other), the semigroups representing the automata are distinct. We show that representation by the transition semigroup is not successful. We then consider a representation of automata by semigroups of partial transformations. We show that in general transition from automata to semigroups by this representation is not successful either. In fact, the only successful transition presented is the transiton to this semigroup of par…

Minimal Forbidden Factors of Circular Words

2017

Minimal forbidden factors are a useful tool for investigating properties of words and languages. Two factorial languages are distinct if and only if they have different (antifactorial) sets of minimal forbidden factors. There exist algorithms for computing the minimal forbidden factors of a word, as well as of a regular factorial language. Conversely, Crochemore et al. [IPL, 1998] gave an algorithm that, given the trie recognizing a finite antifactorial language M, computes a DFA of the language having M as set of minimal forbidden factors. In the same paper, they showed that the obtained DFA is minimal if the input trie recognizes the minimal forbidden factors of a single word. We gener…

A Scheme for Continuous Input to the Tsetlin Machine with Applications to Forecasting Disease Outbreaks

2019

In this paper, we apply a new promising tool for pattern classification, namely, the Tsetlin Machine (TM), to the field of disease forecasting. The TM is interpretable because it is based on manipulating expressions in propositional logic, leveraging a large team of Tsetlin Automata (TA). Apart from being interpretable, this approach is attractive due to its low computational cost and its capacity to handle noise. To attack the problem of forecasting, we introduce a preprocessing method that extends the TM so that it can handle continuous input. Briefly stated, we convert continuous input into a binary representation based on thresholding. The resulting extended TM is evaluated and analyzed…