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28
TreeWalking Pebble Automata
 Jewels are forever, contributions to Theoretical Computer Science in honor of Arto Salomaa
, 1999
"... this paper is to investigate the power of treewalking automata with pebbles. Obviously, the unrestricted use of pebbles leads to a class of tree languages much larger than the regular tree languages, in fact to all tree languages in NSPACE(logn). Thus, we restrict the automaton to the recursive use ..."
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Cited by 38 (2 self)
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this paper is to investigate the power of treewalking automata with pebbles. Obviously, the unrestricted use of pebbles leads to a class of tree languages much larger than the regular tree languages, in fact to all tree languages in NSPACE(logn). Thus, we restrict the automaton to the recursive use of pebbles, in the sense that the life times of pebbles, i.e., the times between dropping a pebble and lifting it again, are properly nested. A similar, but stronger, nesting requirement is studied in [13] for 2way automata on strings. We prove in Section 5 that our restriction indeed guarantees that all tree languages recognized by the treewalking pebble automaton are regular, but we conjecture that the automaton is not powerful enough to recognize all regular tree languages. In Section 6 we generalize the notion of pebble to that of a \setpebble", in such a way that the treewalking setpebble automaton recognizes exactly the regular tree languages.
Extensions of Attribute Grammars for Structured Document Queries
, 1999
"... Document specification languages like for instance XML, model documents using extended contextfree grammars. These differ from standard contextfree grammars in that they allow arbitrary regular expressions on the righthand side of productions. To query such documents, we introduce a new form of a ..."
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Cited by 33 (6 self)
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Document specification languages like for instance XML, model documents using extended contextfree grammars. These differ from standard contextfree grammars in that they allow arbitrary regular expressions on the righthand side of productions. To query such documents, we introduce a new form of attribute grammars (extended AGs) that work directly over extended contextfree grammars rather than over standard contextfree grammars. Viewed as a query language, extended AGs are particularly relevant as they can take into account the inherent order of the children of a node in a document.
Complexity Results for TwoWay and MultiPebble Automata and their Logics
 Theoretical Computer Science
, 1996
"... : Twoway and multipebble automata are considered (the latter appropriately restricted to accept only regular languages), and enriched with additional features, such as nondeterminism and concurrency. We investigate the succinctness of such machines, and the extent to which this succinctness carrie ..."
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Cited by 32 (0 self)
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: Twoway and multipebble automata are considered (the latter appropriately restricted to accept only regular languages), and enriched with additional features, such as nondeterminism and concurrency. We investigate the succinctness of such machines, and the extent to which this succinctness carries over to make the reasoning problem in propositional dynamic logic (PDL) more difficult. The two main results establish that each additional pebble provides inherent exponential power on both fronts. 1 Introduction 1.1 Background This paper continues our work in [H], [DH], [HRV], seeking exponential (or higher) discrepancies in the succinctness of finite automata when augmented with various additional mechanisms. It is wellknown, for example, that NFAs are exponentially more succinct than DFAs, in the following upper and lower bound senses (see [RS], [MF]): (i) Any NFA can be simulated by a DFA with at most an exponential growth in size; (ii) There is a family of regular sets, L n , for ...
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...
Complexity of TwoDimensional Patterns
, 2000
"... In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are wellestablished classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of se ..."
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Cited by 15 (3 self)
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In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are wellestablished classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for twoormoredimensional patterns. We show that several de nitions of "regular language" or "local rule" that are equivalent in d = 1 lead to distinct classes in d 2. We explore the closure properties and computational complexity of these classes, including undecidability and L, NL and NPcompleteness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finitetime images, and limit sets. We show that it is undecidable whether a CA in d 2 has a periodic point of a given peri...
Automata with nested pebbles capture firstorder logic with transitive closure
 Logical Methods in Computer Science
"... Vol. 3 (2:3) 2007, pp. 1–27 ..."
ContextSensitive String Languages and Recognizable Picture Languages
, 1997
"... ... In this article, we prove a similar result: the family of frontiers of recognizable picture languages is exactly the family of contextsensitive languages. ..."
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Cited by 9 (2 self)
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... In this article, we prove a similar result: the family of frontiers of recognizable picture languages is exactly the family of contextsensitive languages.
Attribute Grammars for Unranked Trees as a query language for structured documents
"... Document specification languages, like for instance XML, model documents using extended contextfree grammars. These di#er from standard contextfree grammars in that they allow arbitrary regular expressions on the righthand side of productions. To query such documents, we introduce a new form ..."
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Cited by 7 (3 self)
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Document specification languages, like for instance XML, model documents using extended contextfree grammars. These di#er from standard contextfree grammars in that they allow arbitrary regular expressions on the righthand side of productions. To query such documents, we introduce a new form of attribute grammars (extended AGs) that work directly over extended contextfree grammars rather than over standard contextfree grammars. Viewed as a query language, extended AGs are particularly relevant as they can take into account the inherent order of the children of a node in a document.
Trips on Trees
 ACTA CYBERNETICA
, 1999
"... A "trip" is a triple (g; u; v) where g is, in general, a graph and u and v are nodes of that graph. The trip is from u to v on the graph g. For the special case that g is a tree (or even a string) we investigate ways of specifying and implementing sets of trips. The main result is that ..."
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Cited by 6 (0 self)
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A "trip" is a triple (g; u; v) where g is, in general, a graph and u and v are nodes of that graph. The trip is from u to v on the graph g. For the special case that g is a tree (or even a string) we investigate ways of specifying and implementing sets of trips. The main result is that a regular set of trips, specified as a regular tree language, can be implemented by a treewalking automaton that uses marbles and one pebble.
New Results on Alternating and NonDeterministic TwoDimensional FiniteState Automata
 In: Proceedings STACS 2001, LNCS 2010
, 2001
"... . We resolve several longstanding open questions regarding the power of various types of nitestate automata to recognize \picture languages," i.e. sets of twodimensional arrays of symbols. We show that the languages recognized by 4way alternating nitestate automata (AFAs) are incompara ..."
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Cited by 6 (0 self)
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. We resolve several longstanding open questions regarding the power of various types of nitestate automata to recognize \picture languages," i.e. sets of twodimensional arrays of symbols. We show that the languages recognized by 4way alternating nitestate automata (AFAs) are incomparable to the socalled tiling recognizable languages. Specically, we show that the set of acyclic directed graphs is AFArecognizable but not tiling recognizable, while the set of nonacyclic directed graphs is tiling recognizable but not AFArecognizable. More generally, the complement of an AFArecognizable language is tiling recognizable, and therefore the AFArecognizable languages are not closed under complement. We also show that the set of languages recognized by 4way NFAs is not closed under complement, and that NFAs are more powerful than DFAs, even for languages over one symbol. 1 Introduction Twodimensional words, or \pictures," are rectangular arrays of symbols over a nit...