Locally threshold testable languages in strict sense: Application to the inference problem

Ruiz, José; España, Salvador; Garcia, Pedro Castillo

doi:10.1007/bfb0054072

Cited by 14 publications

(6 citation statements)

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“…A related restriction of the LTT languages that we should mention is that of the locally threshold testable languages in the strict sense (LTTSS) [7,18]. The key difference between these languages and our class LLT is that, in the former, one sets a threshold condition for each infix separately (which corresponds to using multiple counters in their characterization in terms of scanners).…”

Section: The Class Lltmentioning

confidence: 99%

Sublinear-Time Probabilistic Cellular Automata

Modanese¹

2022

Preprint

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We propose and investigate a probabilistic model of sublinear-time one-dimensional cellular automata. In particular, we modify the model of ACA (which are cellular automata that accept if and only if all cells simultaneously accept) so that every cell changes its state not only dependent on the states it sees in its neighborhood but also on an unbiased coin toss of its own. The resulting model is dubbed probabilistic ACA (PACA), accordingly. We consider both one-and two-sided error versions of the model (in the same spirit as the classical Turing machine classes RP and BPP) and establish a separation between the classes of languages they can recognize all the way up to o( √ n) time. We also prove that the derandomization of T (n)-time PACA (to polynomial-time deterministic cellular automata) for various regimes of T (n) = ω(log n) implies non-trivial derandomization results for the class RP (e.g., P = RP). Last but not least, as our main contribution we give a full characterization of the constant-time PACA classes: For one-sided error, the class is equal to that of the deterministic model; that is, we prove that constant-time one-sided error PACA can be fully derandomized with only a constant multiplicative overhead in time complexity. As for two-sided error, we characterize the respective class in terms of a linear threshold condition and prove that it lies in-between the class of strictly locally testable languages (SLT) and that of locally threshold testable languages (LTT) while being incomparable to the locally testable languages (LT). ACM Subject Classification Theory of computation → Formal languages and automata theory Keywords and phrases Cellular automata, local computation, probabilistic modelsAcknowledgements I would like to thank Thomas Worsch for the many helpful discussions and feedback.

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Section: The Class Lltmentioning

confidence: 99%

Sublinear-Time Probabilistic Cellular Automata

Modanese¹

2022

Preprint

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“…The locally threshold testable languages introduced by Beauquier and Pin [1] now have various applications [8], [15], [16]. In particular, stochastic locally threshold testable languages, also known as n − grams, are used in pattern recognition and in speech recognition, both in acoustic-phonetics decoding and in language modelling [15].…”

Section: Introductionmentioning

confidence: 99%

Reducing the time complexity of testing for local threshold testability

Trahtman

2004

Theoretical Computer Science

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A locally threshold testable language L is a language with the property that for some nonnegative integers k and l and for some word u from L, a word v belongs to L iff (1) the prefixes [suffixes] of length k − 1 of words u and v coincide, (2) the numbers of occurrences of every factor of length k in both words u and v are either the same or greater than l − 1. A deterministic finite automaton is called locally threshold testable if the automaton accepts a locally threshold testable language for some l and k. New necessary and sufficient conditions for a deterministic finite automaton to be locally threshold testable are found. On the basis of these conditions, we modify the algorithm to verify local threshold testability of the automaton and to reduce the time complexity of the algorithm. The algorithm is implemented as a part of the C/C ++ package TESTAS.

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“…The locally threshold testable languages were introduced by Beauquier and Pin [4]. These languages generalize the concept of locally testable language and have been studied extensively in recent years (see [5], [22], [27], [33], [34]), [25].…”

Section: Introductionmentioning

confidence: 99%

“…An important reason to study locally threshold testable languages is the possibility of being used in pattern recognition [10], [12], [25]. Stochastic locally threshold testable languages, also known as N −grams are used in pattern recognition, particulary in speech recognation, both in acoustic-phonetics decoding as in language modeling [32].…”

Section: Introductionmentioning

confidence: 99%

“…Stochastic locally threshold testable languages, also known as N −grams are used in pattern recognition, particulary in speech recognation, both in acoustic-phonetics decoding as in language modeling [32]. An application of these languages to the inference problem considered in [25]. The syntactic characterization of locally threshold testable languages one can find in [4]:…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm to Verify Local Threshold Testability of Deterministic Finite Automata

Trahtman¹

2001

Lecture Notes in Computer Science

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A locally threshold testable language L is a language with the property that for some nonnegative integers k and l, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of length k − 1 and (2) the set of intermediate substrings of length k of the word u where the sets of substrings occurring at least j times are the same, for j ≤ l. For given k and l the language is called l-threshold k-testable. A finite deterministic automaton is called l-threshold k-testable if the automaton accepts a l-threshold k-testable language. In this paper, the necessary and sufficient conditions for an automaton to be locally threshold testable are found. We introduce the first polynomial time algorithm to verify local threshold testability of the automaton based on this characterization. New version of polynomial time algorithm to verify the local testability will be presented too.

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Locally threshold testable languages in strict sense: Application to the inference problem

Cited by 14 publications

References 10 publications

Sublinear-Time Probabilistic Cellular Automata

Sublinear-Time Probabilistic Cellular Automata

Reducing the time complexity of testing for local threshold testability

An Algorithm to Verify Local Threshold Testability of Deterministic Finite Automata

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