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28
Twovariable logic on data words
, 2007
"... In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable firstorder ..."
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Cited by 35 (4 self)
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In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the twovariable firstorder logic FO 2 (∼,<,+1) is decidable over finite and over infinite data words, where ∼ is a binary predicate testing the data value equality and +1, < are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable.
An extension of data automata that captures XPath
, 2010
"... Abstract—We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automatatheoretic approach may be applied to answer decidability and expressibility questions for XPath. Finally, ..."
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Cited by 16 (1 self)
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Abstract—We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automatatheoretic approach may be applied to answer decidability and expressibility questions for XPath. Finally, we use the newly introduced automata as a common framework to classify existing automata on data words and trees, including data automata, register automata and alternating register automata. KeywordsRegular XPath, data automata, register automata. I.
Temporal Logics on Words with Multiple Data Values
 In FSTTCS 2010
"... The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)pairs at each position. It considers a basic logic which is a semantical fragment of the logic LTL ↓ 1 of Demri and Lazic with operators for navigation into the future an ..."
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The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)pairs at each position. It considers a basic logic which is a semantical fragment of the logic LTL ↓ 1 of Demri and Lazic with operators for navigation into the future and the past. By reduction to the emptiness problem for data automata it is shown that this basic logic is decidable. Whereas the basic logic only allows navigation to positions where a fixed data value occurs, extensions are studied that also allow navigation to positions with different data values. Besides some undecidable results it is shown that the extension by a certain UNTILoperator with an inequality target condition remains decidable.
Graph reachability and pebble automata over infinite alphabets
 In LICS’09
"... Abstract—We study the graph reachability problem as a language over an infinite alphabet. Namely, we view a word of even length a0b0 ···anbn over an infinite alphabet as a directed graph with the symbols that appear in a0b0 ···anbn as the vertices and (a0,b0),...,(an,bn) as the edges. We prove that ..."
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Abstract—We study the graph reachability problem as a language over an infinite alphabet. Namely, we view a word of even length a0b0 ···anbn over an infinite alphabet as a directed graph with the symbols that appear in a0b0 ···anbn as the vertices and (a0,b0),...,(an,bn) as the edges. We prove that for any positive integer k, k pebbles are sufficient for recognizing the existence of a path of length 2 k − 1 from the vertex a0 to the vertex bn, but are not sufficient for recognizing the existence of a path of length 2 k+1 −2 from the vertex a0 to the vertex bn. Based on this result, we establish a number of relations among some classes of languages over infinite alphabets. KeywordsGraph reachability; pebble automata; infinite alphabets I.
Regular Functions, Cost Register Automata, and Generalized MinCost Problems
, 2012
"... Motivated by the successful application of the theory of regular languages to formal verification of finitestate systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can provide a foundation for analyzing quantitative properties o ..."
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Motivated by the successful application of the theory of regular languages to formal verification of finitestate systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can provide a foundation for analyzing quantitative properties of finitestate systems. In this paper, we propose a deterministic model for associating costs with strings that is parameterized by operations of interest (such as addition, scaling, and min), a notion of regularity that provides a yardstick to measure expressiveness, and study decision problems and theoretical properties of resulting classes of cost functions. Our definition of regularity relies on the theory of stringtotree transducers, and allows associating costs with events that are conditional upon regular properties of future events. Our model of cost register automata allows computation of regular functions using multiple “writeonly ” registers whose values can be combined using the allowed set of operations. We show that classical shortestpath algorithms as well as algorithms designed for computing discounted costs, can be adopted for solving the mincost problems for the more general classes of functions specified in our model. Cost register automata with min and increment give a deterministic model that is equivalent to weighted automata, an extensively studied nondeterministic model, and this 1.1
Algorithmic Analysis of ArrayAccessing Programs
"... For programs whose data variables range over Boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this paper, we consider algorithmic verification of programs that use Boolean variables, and in addition, access a singl ..."
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For programs whose data variables range over Boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this paper, we consider algorithmic verification of programs that use Boolean variables, and in addition, access a single array whose length is potentially unbounded, and whose elements range over pairs from Σ × D, where Σ is a finite alphabet and D is a potentially unbounded data domain. We show that the reachability problem, while undecidable in general, is (1) PSPACEcomplete for programs in which the arrayaccessing forloops are not nested, (2) solvable in EXPSPACE for programs with arbitrarily nested loops if array elements range over a finite data domain, and (3) decidable for a restricted class of programs with doublynested loops. The third result establishes connections to automata and logics defining languages over data words.
Feasible Automata for TwoVariable Logic with Successor on Data Words
"... We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data ..."
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We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data automata. It is strictly less expressive than data automata and the expressive power is incomparable with register automata. The expressive power of weak data automata corresponds exactly to existential monadic second order logic with successor +1 and data value equality ∼, EMSO 2 (+1,∼). It follows from previous work, David, et. al. in 2010, that the nonemptiness problem for weak data automata can be decided in 2NEXPTIME. Furthermore, we study weak Büchi automata on data ωstrings. They can be characterized by the extension of EMSO 2 (+1,∼) with existential quantifiers for infinite sets. Finally, the same complexity bound for its nonemptiness problem is established by a nondeterministic polynomial time reduction to the nonemptiness problem of weak data automata.
Alternating automata on data trees and XPath satisfiability
 ACM Transactions on Computational Logic (TOCL
"... A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (“datum”) from an infinite set, where the latter can only be compared for equality. The paper considers alternating automata on data trees that can move downward and rightward, and ..."
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A data tree is an unranked ordered tree whose every node is labelled by a letter from a finite alphabet and an element (“datum”) from an infinite set, where the latter can only be compared for equality. The paper considers alternating automata on data trees that can move downward and rightward, and have one register for storing data. The main results are that nonemptiness over finite data trees is decidable but not primitive recursive, and that nonemptiness of safety automata is decidable but not elementary. The proofs use nondeterministic tree automata with faulty counters. Allowing upward moves, leftward moves, or two registers, each cause undecidability. As corollaries, decidability is obtained for two datasensitive fragments of the XPath query language.
On pebble automata for data languages with decidable emptiness problem
 Journal of Computer and Systems Sciences
"... Abstract. In this paper we study a subclass of pebble automata (PA) for data languages for which the emptiness problem is decidable. Namely, we show that the emptiness problem for weak 2pebble automata is decidable, while the same problem for weak 3pebble automata is undecidable. We also introduce ..."
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Abstract. In this paper we study a subclass of pebble automata (PA) for data languages for which the emptiness problem is decidable. Namely, we show that the emptiness problem for weak 2pebble automata is decidable, while the same problem for weak 3pebble automata is undecidable. We also introduce the socalled top view weak PA. Roughly speaking, top view weak PA are weak PA where the equality test is performed only between the data values seen by the two most recently placed pebbles. The emptiness problem for this model is still decidable. 1