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Regular expressions are used in many practical applications. Practical regular expressions are commonly called "regex". It is known that regex are different from regular expressions. In this paper, we give regex a formal treatment. We make a distinction between regex and extended regex; while regex ...
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We present a fast incremental algorithm for constructing minimal DFCA for a given language. Since it was shown that the DFCA for a language L can have less states than the DFA for L, this technique seen-is to be the best choice for incrementally building the automaton for a large language, especiall...
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We introduce a new variant of the heavily studied model of H systems. The new variant will use an external factor to determine the set of the active splicing rules. We improve the best known universality result for time-varying H systems with respect to the diameter of such a system and we prove tha...
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In this paper we study the language of the words that, for a given language L, distinguish between pairs of different left-quotients of L. We characterize this distinguishability operation, show that its iteration has always a fixed point, and we generalize this result to operations derived from clo...
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We present a fast incremental algorithm for constructing minimal Deterministic Finite Cover Automata (DFCA) for a given language. Since it was shown that the minimal DFCA for a language L has less states than the minimal Deterministic Finite Automata (DFA) for the same language L, this technique see...
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Quite often, trivial problems stated for deterministic finite automata (DFA) are surprisingly difficult for the non-deterministic case (NFA). In any non-minimal DFA for a given regular language, we can find two equivalent states which can be “merged” without changing the accepted language. This ...
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A cover-automaton A of a finite language L⊆Σ∗ is a finite deterministic automaton (DFA) that accepts all words in L and possibly other words that are longer than any word in L. A minimal deterministic finite cover automaton (DFCA) of a finite language L usually has a smaller size than a minimal...
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A string x is random according to Kolmogorov [10] if, given its length, there is no stringy, sensibly shorter than x, by means of which a universal partial recursive function could produce x. This remarkable definition has been validated in several ways (see [12, 14, 2, 11]) including a topological ...
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The nuclear reaction O-18 (d, 2n) F-18 and the separation of F-18 from the irradiated samples have been studied. For this reaction liquid H2O samples were irradiated with deuterons beam in the stainless steel cells cooled with water. The formed positron emiting F-18 was separated from (H2O)-O-18 by ...
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We define the pattern expressions as an extension of both regular expressions and patterns. We prove several properties of the new family of languages, similar to those of extended regex languages [Câmpeanu et al., Int. J. Found. Comput. Sci. 14 (6) (2003) 1007–1018]. We also define an automata s...
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Regex are used in many programs such as Perl, Awk, Python, egrep, vi, emacs etc. It is known that regex are different from regular expressions. In this paper, we give regex a formal treatment. We make a distinction between regex and extended regex; while regex present regular languages, extended reg...
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In this paper we consider the transformation from (minimal) non-deterministic finite automata (NFAs) to deterministic finite cover automata (DFCAs). We want to compare the two equivalent accepting devices with respect to their number of states; this becomes in fact a comparison between the expressio...
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We study the shuffle quotient operation and introduce equivalence relations it defines with respect to a (regular) language. Corresponding to an arbitrary shuffle decomposition we construct a normalized decomposition that is defined in terms of maximal languages. Using closure properties of the norm...
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We introduce a right congruence relation that is the analogy of the Nerode congruence when catenation is replaced by shuffle. Using this relation we show that for certain subclasses of regular languages the shuffle decomposition problem is decidable. We show that shuffle decomposition is undecidable...
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Finite Deterministic Cover Automata (DFCA) can be obtained from Deterministic Finite Automata (DFA) using the similarity relation-Since the similarity relation is not an equivalence relation, the minimal DFCA for a finite language is usually not unique. We count the number of minimal DFCA that can b...
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In this paper we prove a lower bound for the maximum state complexity of Deterministic Finite Cover Automata (DFCAs) obtained from Non-deterministic Finite Automata (NFAs) of a given state complexity n, in case of a binary alphabet. We show, for binary alphabets, that the difference between maximum ...
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