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31
Typechecking TopDown Uniform Unranked Tree Transducers
 in 9th International Conference on Database Theory, ser. LNCS
"... We investigate the typechecking problem for XML queries: statically verifying that every answer to a query conforms to a given output schema, for inputs satisfying a given input schema. As typechecking quickly turns undecidable for query languages capable of testing equality of data values, we retur ..."
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Cited by 31 (3 self)
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We investigate the typechecking problem for XML queries: statically verifying that every answer to a query conforms to a given output schema, for inputs satisfying a given input schema. As typechecking quickly turns undecidable for query languages capable of testing equality of data values, we return to the limited framework where we abstract XML documents as labeled ordered trees. We focus on simple topdown recursive transformations motivated by XSLT and structural recursion on trees. We parameterize the problem by several restrictions on the transformations (deleting, nondeleting, bounded width) and consider both tree automata and DTDs as output schemas. The complexity of the typechecking problems in this scenario range from ptime to exptime.
Complexity of decision problems for simple regular expressions
 IN PROCEEDINGS OF THE 29TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 2004
, 2004
"... We study the complexity of the inclusion, equivalence, and intersection problem for simple regular expressions arising in practical XML schemas. These basically consist of the concatenation of factors where each factor is a disjunction of strings possibly extended with ‘∗ ’ or ‘?’. We obtain lower ..."
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Cited by 27 (12 self)
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We study the complexity of the inclusion, equivalence, and intersection problem for simple regular expressions arising in practical XML schemas. These basically consist of the concatenation of factors where each factor is a disjunction of strings possibly extended with ‘∗ ’ or ‘?’. We obtain lower and upper bounds for various fragments of simple regular expressions. Although we show that inclusion and intersection are already intractable for very weak expressions, we also identify some tractable cases. For equivalence, we only prove an initial tractability result leaving the complexity of more general cases open. The main motivation for this research comes from database theory, or more specifically XML and semistructured data. We namely show that all lower and upper bounds for inclusion and equivalence, carry over to the corresponding decision problems for extended contextfree grammars and singletype tree grammars, which are abstractions of DTDs and XML Schemas, respectively. For intersection, we show that the complexity only carries over for DTDs.
The Liberty structural specification language: a highlevel modeling language for component reuse
 in 2004 ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI'04
, 2004
"... Rapid exploration of the design space with simulation models is essential for quality hardware systems research and development. Despite striking commonalities across hardware systems, designers routinely fail to achieve high levels of reuse across models constructed in existing generalpurpose and ..."
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Cited by 26 (7 self)
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Rapid exploration of the design space with simulation models is essential for quality hardware systems research and development. Despite striking commonalities across hardware systems, designers routinely fail to achieve high levels of reuse across models constructed in existing generalpurpose and domainspecific languages. This lack of reuse adversely impacts hardware system design by slowing the rate at which ideas are evaluated. This paper presents an examination of existing languages to reveal their fundamental limitations regarding reuse in hardware modeling. With this understanding, a solution is described in the context of the design and implementation of the Liberty Structural Specification Language (LSS), the input language for a publicly available highlevel digitalhardware modeling tool called the Liberty Simulation Environment. LSS is the first language to enable lowoverhead reuse by simultaneously supporting static inference based on hardware structure and flexibility via parameterizable structure. Through LSS, this paper also introduces a new type inference algorithm and a new programming language technique, called usebased specialization, which, in a manner analogous to type inference, customizes reusable components by statically inferring structural properties that otherwise would have had to have been specified manually.
Optimizing schema languages for XML: Numerical constraints and interleaving
 ICDT
, 2007
"... The presence of a schema offers many advantages in processing, translating, querying, and storage of XML data. Basic decision problems like equivalence, inclusion, and nonemptiness of intersection of schemas form the basic building blocks for schema optimization and integration, and algorithms for ..."
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Cited by 20 (6 self)
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The presence of a schema offers many advantages in processing, translating, querying, and storage of XML data. Basic decision problems like equivalence, inclusion, and nonemptiness of intersection of schemas form the basic building blocks for schema optimization and integration, and algorithms for static analysis of transformations. It is thereby paramount to establish the exact complexity of these problems. Most common schema languages for XML can be adequately modeled by some kind of grammar with regular expressions at righthand sides. In this paper, we observe that apart from the usual regular operators of union, concatenation and Kleenestar, schema languages also allow numerical occurrence constraints and interleaving operators. Although the expressiveness of these operators remain within the regular languages, their presence or absence has significant impact on the complexity of the basic decision problems. We present a complete overview of the complexity of the basic decision problems for DTDs, XSDs and Relax NG with regular expressions incorporating numerical occurrence constraints and interleaving. We also discuss chain regular expressions and the complexity of the schema simplification problem incorporating the new operators.
Ground reducibility is EXPTIMEcomplete
 Information and Computation
, 1997
"... Abstract. We prove that ground reducibility is EXPTIMEcomplete in the general case. EXPTIMEhardness is proved by encoding the emptiness problem for the intersection of recognizable tree languages. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an aut ..."
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Cited by 19 (9 self)
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Abstract. We prove that ground reducibility is EXPTIMEcomplete in the general case. EXPTIMEhardness is proved by encoding the emptiness problem for the intersection of recognizable tree languages. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an automaton with disequality constraints AR,t to a rewrite system R and a term t. This automaton is deterministic and accepts at least one term iff t is not ground reducible by R. The number of states of AR,t is O(2 �R��t � ) and the size of its constraints is polynomial in the size of R, t. Then we prove some new pumping lemmas, using a total ordering on the computations of the automaton. Thanks to these lemmas, we can show that emptiness for an automaton with disequality constraints can be decided in a time which is polynomial in the number of states and exponential in the size of the constraints. Altogether, we get a simply exponential time deterministic algorithm for ground reducibility decision. 1
Tree Automata with Equality Constraints Modulo Equational Theories
 Proceedings of 3rd International Joint Conference on Automated Reasoning, IJCAR, volume 4130 of Lecture Notes in Artificial Intelligence
, 2006
"... Abstract. This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that these classes have a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn ..."
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Cited by 17 (3 self)
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Abstract. This paper presents new classes of tree automata combining automata with equality test and automata modulo equational theories. We believe that these classes have a good potential for application in e.g. software verification. These tree automata are obtained by extending the standard Horn clause representations with equational conditions and rewrite systems. We show in particular that a generalized membership problem (extending the emptiness problem) is decidable by proving that the saturation of tree automata presentations with suitable paramodulation strategies terminates. Alternatively our results can be viewed as new decidable classes of firstorder formula. 1
Codefinite Set Constraints
 Proceedings of the 9th International Conference on Rewriting Techniques and Applications, volume 1379 of LNCS
"... In this paper, we introduce the class of codefinite set constraints. This is a natural subclass of set constraints which, when satisfiable, have a greatest solution. It is practically motivated by the setbased analysis of logic programs with the greatestmodel semantics. We present an algorithm so ..."
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Cited by 16 (8 self)
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In this paper, we introduce the class of codefinite set constraints. This is a natural subclass of set constraints which, when satisfiable, have a greatest solution. It is practically motivated by the setbased analysis of logic programs with the greatestmodel semantics. We present an algorithm solving codefinite set constraints and show that their satisfiability problem is DEXPTIMEcomplete. 1 Introduction Set constraints and setbased analysis form an established research topic. It combines theoretical investigations ranging from expressiveness and decidability to program semantics and domain theory, with direct practical applications to type inference, optimization and verification of imperative, functional, logic and reactive programs (see [1, 14, 20] for overviews). In setbased analysis, the problem of reasoning about runtime properties of programs is transferred to the problem of solving set constraints. The design of a system for a particular program analysis problem (for a...
Directional Type Inference for Logic Programs
, 1998
"... . We follow the setbased approach to directional types proposed by Aiken and Lakshman [1]. Their type checking algorithm works via set constraint solving and is sound and complete for given discriminative types. We characterize directional types in modeltheoretic terms. We present an algorithm ..."
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Cited by 16 (6 self)
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. We follow the setbased approach to directional types proposed by Aiken and Lakshman [1]. Their type checking algorithm works via set constraint solving and is sound and complete for given discriminative types. We characterize directional types in modeltheoretic terms. We present an algorithm for inferring directional types. The directional type that we derive from a logic program P is uniformly at least as precise as any discriminative directional type of P, i.e., any directional type out of the class for which the type checking algorithm of Aiken and Lakshman is sound and complete. We improve their algorithm as well as their lower bound and thereby settle the complexity (DEXPTIMEcomplete) of the corresponding problem. 1 Introduction Directional types form a type system for logic programs which is based on the view of a predicate as a directional procedure which, when applied to a tuple of input terms, generates a tuple of output terms. There is a rich literature on ty...
Unification in a Description Logic with Transitive Closure of Roles
, 2001
"... Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL 0 , which allows for conjunction, value restriction, and the top concept only, is already ExpTime comple ..."
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Cited by 13 (4 self)
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Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL 0 , which allows for conjunction, value restriction, and the top concept only, is already ExpTime complete. The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles. It also shows that matching (which is polynomial in FL 0 ) is PSpacecomplete in the extended description logic.