Results 1  10
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27
Query Automata
 In Proceedings of the Eighteenth ACM Symposium on Principles of Database Systems
, 1999
"... A main task in document transformation and information retrieval is locating subtrees satisfying some pattern. Therefore, unary queries, i.e., queries that map a tree to a set of its nodes, play an important role in the context of structured document databases. We want to understand how the natu ..."
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Cited by 29 (8 self)
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A main task in document transformation and information retrieval is locating subtrees satisfying some pattern. Therefore, unary queries, i.e., queries that map a tree to a set of its nodes, play an important role in the context of structured document databases. We want to understand how the natural and wellstudied computation model of tree automata can be used to compute such queries. We dene a query automaton (QA) as a deterministic twoway nite automaton over trees that has the ability to select nodes depending on the state and the label at those nodes. We study QAs over ranked as well as over unranked trees. Unranked trees dier from ranked ones in that there is no bound on the number of children of nodes. We characterize the expressiveness of the dierent formalisms as the unary queries denable in monadic secondorder logic (MSO). Surprisingly, in contrast to the ranked case, special stay transitions had to be added to QAs over unranked trees to capture MSO. We es...
Numeration systems on a regular language
 Theory Comput. Syst
"... Generalizations of linear numeration systems in which IN is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of numeration, we show that ultimately periodic sets are recognizable. We also study t ..."
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Cited by 11 (5 self)
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Generalizations of linear numeration systems in which IN is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of numeration, we show that ultimately periodic sets are recognizable. We also study the translation and the multiplication by constants as well as the orderdependence of the recognizability. 1
On the Sequentiality of the Successor Function
, 1997
"... Let U be a strictly increasing sequence of integers. By a greedy algorithm, every nonnegative integer has a greedy Urepresentation. The successor function maps the greedy Urepresentation of N onto the greedy Urepresentation of N+1. We characterize the sequences U such that the successor functi ..."
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Cited by 10 (1 self)
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Let U be a strictly increasing sequence of integers. By a greedy algorithm, every nonnegative integer has a greedy Urepresentation. The successor function maps the greedy Urepresentation of N onto the greedy Urepresentation of N+1. We characterize the sequences U such that the successor function associated to U is a left, resp. a right sequential function. We also show that the odometer associated to U is continuous if and only if the successor function is right sequential.
On the Automata Size for Presburger Arithmetic
 In Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS 2004
, 2004
"... Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Pr ..."
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Cited by 9 (1 self)
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Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Presburger arithmetic formula is triple exponentially bounded in the length of the formula. This upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method. We also show that this triple exponential bound is tight (even for nondeterministic automata). Moreover, we provide optimal automata constructions for linear equations and inequations.
State complexity of shuffle on trajectories
 In Descriptional Complexity of Formal Systems (DCFS) (2002
, 2004
"... Abstract It is easy to get an upper bound for the state complexity of shuffle on trajectories that generalizes the bound for unrestricted shuffle. We establish improved bounds for slender trajectories. For trajectories with USL index 1 (or 1thin trajectories) we obtain an asymptotically tight lower ..."
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Cited by 6 (4 self)
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Abstract It is easy to get an upper bound for the state complexity of shuffle on trajectories that generalizes the bound for unrestricted shuffle. We establish improved bounds for slender trajectories. For trajectories with USL index 1 (or 1thin trajectories) we obtain an asymptotically tight lower bound when the state complexity of the trajectory grows with respect to the state complexity of the component languages. Some estimations are improved by considering nondeterministic state complexity. 1 Introduction The notion of shuffle on trajectories was introduced as an extension of the existing notions of shuffle by Mateescu et al. [5] to provide an abstraction of parallel composition of words, an important operation in parallel computation.
A Characterization of PolySlender ContextFree Languages
 Inform. Appl
, 2000
"... For a nonnegative integer k, we say that a language L is kpolyslender if the number of words of length n in L is of order O(n k ). We give a precise characterization of the k polyslender contextfree languages. The wellknown characterization of the kpolyslender regular languages is an im ..."
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Cited by 5 (1 self)
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For a nonnegative integer k, we say that a language L is kpolyslender if the number of words of length n in L is of order O(n k ). We give a precise characterization of the k polyslender contextfree languages. The wellknown characterization of the kpolyslender regular languages is an immediate consequence of ours. Keywords: contextfree language, polyslender language, Dyck loop Introduction An infinite sequence (#L (n)) n0 can be associated in a natural way to a language L: #L (n) is the number of words of length n in L. The idea is by no means new; for instance, in the first ICALP, Berstel [3] considered the notion of the population function of a language L which associates, to every n, the number of words of length at most n in L. The notion of the number of words of the same length is certainly very basic one in language theory and this is why some results have been proved several times. We recall briefly in the following the history of such results. When #L (n) is ...
On the cost and complexity of the successor function
 In Proc. WORDS 2007
, 2009
"... Abstract. For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the nth word of a genealogically ordered language L onto the (n+1)th word of L. We show that, if t ..."
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Cited by 4 (3 self)
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Abstract. For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the nth word of a genealogically ordered language L onto the (n+1)th word of L. We show that, if the ratio of the number of elements of length n +1overthenumber of elements of length n of the language has a limit β>1, then the amortized cost of the successor function is equal to β/(β − 1). From this, we deduce the value of the amortized cost for several classes of numeration systems (integer base systems, canonical numeration systems associated with a Parry number, abstract numeration systems built on a rational language, and rational base numeration systems). 1
RADIX ENUMERATION OF RATIONAL LANGUAGES
 THEORETICAL INFORMATICS AND APPLICATIONS
, 1999
"... We prove that the function that maps a word of a rational language onto its successor for the radix order in this language is a finite union of cosequential functions. ..."
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Cited by 4 (1 self)
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We prove that the function that maps a word of a rational language onto its successor for the radix order in this language is a finite union of cosequential functions.
Hairpin structures defined by DNA trajectories
 C. MAO AND T. YOKOMORI (EDS), PROCEEDINGS OF DNA COMPUTING 12, LNCS 4287
, 2006
"... We examine scattered hairpins, which are structures formed when a single strand folds into a partially hybridized stem and a loop. To specify different classes of hairpins, we use the concept of DNA trajectories, which allows precise descriptions of valid bonding patterns on the stem of the hairpin. ..."
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Cited by 3 (0 self)
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We examine scattered hairpins, which are structures formed when a single strand folds into a partially hybridized stem and a loop. To specify different classes of hairpins, we use the concept of DNA trajectories, which allows precise descriptions of valid bonding patterns on the stem of the hairpin. DNA trajectories have previously been used to describe bonding between separate strands. We are interested in the mathematical properties of scattered hairpins described by DNA trajectories. We examine the complexity of set of hairpinfree words described by a set of DNA trajectories. In particular, we consider the closure properties of language classes under sets of DNA trajectories of differing complexity. We address decidability of recognition problems for hairpin structures.