Automata and Logics for Words and Trees over an Infinite Alphabet

Segoufin, Luc

doi:10.1007/11874683_3

Cited by 142 publications

(149 citation statements)

References 32 publications

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“…Existing related models [8,22] feature transitions of a more compound shape, which can be readily translated into sequences of PDRS transitions.…”

Section: Basic Definitionsmentioning

confidence: 99%

“…Such a theory will expose the limits of this model of computation and establish a complexity-theoretic guide for applications. A lot of the groundwork, surveyed in [22,3], was already dedicated to uncovering a notion of "regularity" in the infinite-alphabet case. Very early in that work, a way was proposed to extend the concept of finite memory to infinite alphabets which consisted in introducing a fixed number of registers for storing elements of the alphabet [13].…”

Section: Introductionmentioning

confidence: 99%

“…Later, Segoufin presented a similar definition in [22], albeit couched in a way suitable to process data words. Our paper is devoted to studying exactly such context-free computational scenarios through an investigation of pushdown register systems (PDRS), devices in which registers are integrated with a pushdown store.…”

Section: Introductionmentioning

confidence: 99%

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Reachability in Pushdown Register Automata

Murawski

Ramsay

Tzevelekos

2014

Mathematical Foundations of Computer Science 2014

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We investigate reachability in pushdown automata over infinite alphabets. We show that, in terms of reachability/emptiness, these machines can be faithfully represented using only 3r elements of the alphabet, where r is the number of registers. We settle the complexity of associated reachability/emptiness problems. In contrast to register automata, the emptiness problem for pushdown register automata is EXPTIME-complete, independent of the register storage policy used. We also solve the global reachability problem by representing pushdown configurations with a special register automaton. Finally, we examine extensions of pushdown storage to higher orders and show that reachability is undecidable at order 2.

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“…Existing related models [8,22] feature transitions of a more compound shape, which can be readily translated into sequences of PDRS transitions.…”

Section: Basic Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reachability in Pushdown Register Automata

Murawski

Ramsay

Tzevelekos

2014

Mathematical Foundations of Computer Science 2014

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“…On the other hand, to prove decidability, we show that (in the relevant cases) the corresponding strategies can be related to context-free languages over infinite alphabets. More precisely, we develop a routine which, starting from program phrases, can construct variants of pushdown register automata [13] that represent the associated game semantics. In this way, the problem is ultimately reduced to emptiness testing for this class of automata, which is known to be decidable.…”

Section: Introductionmentioning

confidence: 99%

Game Semantic Analysis of Equivalence in IMJ

Murawski

Ramsay

Tzevelekos

2015

Automated Technology for Verification and Analysis

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Abstract. Using game semantics, we investigate the problem of verifying contextual equivalences in Interface Middleweight Java (IMJ), an imperative object calculus in which program phrases are typed using interfaces. Working in the setting where data types are non-recursive and restricted to finite domains, we identify the frontier between decidability and undecidability by reference to the structure of interfaces present in typing judgments. In particular, we show how to determine the decidability status of problem instances (over a fixed type signature) by examining the position of methods inside the term type and the types of its free identifiers. Our results build upon the recent fully abstract game semantics of IMJ. Decidability is proved by translation into visibly pushdown register automata over infinite alphabets with fresh-input recognition.

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“…Different models of automata which process words over infinite alphabets have been proposed and studied in the literature (see, for instance, the surveys [6,7]). Pebble automata [8] use special markers to annotate locations in a data word.…”

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confidence: 99%

Automata vs. Logics on Data Words

Benedikt

Ley

Puppis

2010

Computer Science Logic

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Abstract. The relationship between automata and logics has been investigated since the 1960s. In particular, it was shown how to determine, given an automaton, whether or not it is definable in first-order logic with label tests and the order relation, and for first-order logic with the successor relation. In recent years, there has been much interest in languages over an infinite alphabet. Kaminski and Francez introduced a class of automata called finite memory automata (FMA), that represent a natural analog of finite state machines. A FMA can use, in addition to its control state, a (bounded) number of registers to store and compare values from the input word. The class of data languages recognized by FMA is incomparable with the class of data languages defined by firstorder formulas with the order relation and an additional binary relation for data equality. We first compare the expressive power of several variants of FMA with several data word logics. Then we consider the corresponding decision problem: given an automaton A and a logic, can the language recognized by A be defined in the logic? We show that it is undecidable for several variants of FMA, and then investigate the issue in detail for deterministic FMA. We show the problem is decidable for first-order logic with local data comparisons -an analog of first-order logic with successor. We also show instances of the problem for richer classes of first-order logic that are decidable.Logics are natural ways of specifying decision problems on discrete structures, while automata represent natural processing models. On finite words from a fixed (finite) alphabet, Büchi [1] showed that monadic second-order logic has the same expressiveness as deterministic finite state automata, while results of Schützenberger and McNaughton and Papert showed that first-order logic with the label and order predicates has the same expressiveness as counter-free automata [2,3]. The latter theorem gives a decidable characterization of which automata correspond to first-order sentences. Decidable characterizations have also been given for first-order logic with the label and successor predicates [4]. These characterizations have been extended to many other contexts; for example there are characterizations of the tree automata that correspond to sentences in logics on trees [5].Automata processing finite words over infinite alphabets (so called data words) are attracting significant interest from the database and verification communities, since they can be often used as low-level formalisms for representing and reasoning about data streams, program traces, and serializations of structured documents. Moreover, properties specified using high-level formalisms (for

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Automata and Logics for Words and Trees over an Infinite Alphabet

Cited by 142 publications

References 32 publications

Reachability in Pushdown Register Automata

Reachability in Pushdown Register Automata

Game Semantic Analysis of Equivalence in IMJ

Automata vs. Logics on Data Words

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