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15
Monadic Datalog and the Expressive Power of Languages for Web Information Extraction
 J. ACM
, 2002
"... Research on information extraction from Web pages (wrapping) has seen much activity in recent times (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, w ..."
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Cited by 75 (11 self)
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Research on information extraction from Web pages (wrapping) has seen much activity in recent times (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, we first study monadic datalog as a wrapping language (over ranked or unranked tree structures). Using previous work by Neven and Schwentick, we show that this simple language is equivalent to full monadic second order logic (MSO) in its ability to specify wrappers. We believe that MSO has the right expressiveness required for Web information extraction and thus propose MSO as a yardstick for evaluating and comparing wrappers. Using the above result, we study the kernel fragment Elog of the Elog wrapping language used in the Lixto system (a visual wrapper generator). The striking fact here is that Elog exactly captures MSO, yet is easier to use. Indeed, programs in this language can be entirely visually specified. We also formally compare Elog to other wrapping languages proposed in the literature.
Conjunctive Queries over Trees
, 2004
"... We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structures are represented using "axis relations" such as "child", "descendant", and "following" (we consider a superset of the XPath axes) as well as unary relations for node labels. (Cyc ..."
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Cited by 63 (7 self)
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We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structures are represented using "axis relations" such as "child", "descendant", and "following" (we consider a superset of the XPath axes) as well as unary relations for node labels. (Cyclic) conjunctive queries over trees occur in a wide range of data management scenarios related to XML, the Web, and computational linguistics. We establish a framework for characterizing structures representing trees for which conjunctive queries can be evaluated e# ciently. Then we completely chart the tractability frontier of the problem for our axis relations, i.e., we find all subsetmaximal sets of axes for which query evaluation is in polynomial time. All polynomialtime results are obtained immediately using the proof techniques from our framework. Finally, we study the expressiveness of conjunctive queries over trees and compare it to the expressive power of fragments of XPath. We show that for each conjunctive query, there is an equivalent acyclic positive query (i.e., a set of acyclic conjunctive queries), but that in general this query is not of polynomial size.
Using Program Schemes to Logically Capture PolynomialTime on Certain Classes of Structures
 London Mathematical Society Journal of Computation and Mathematics
, 1998
"... We continue the study of the expressive power of certain classes of program schemes on finite structures, in relation to more mainstream logics studied in finite model theory and to computational complexity. We show that there exists a program scheme, whose constructs are assignments and whileloops ..."
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Cited by 5 (5 self)
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We continue the study of the expressive power of certain classes of program schemes on finite structures, in relation to more mainstream logics studied in finite model theory and to computational complexity. We show that there exists a program scheme, whose constructs are assignments and whileloops with quantifierfree tests and which has access to a stack, that can solve a Pcomplete problem, the deterministic path system problem, even in the absence of nondeterminism so long as problem instances are presented in a functional style. Our proof leans heavily on Cook's proof that the classes of formal languages accepted by deterministic and nondeterministic pushdown automata coincide. However, we then show how our program scheme in the above rather esoteric result can be used to build a successor relation in certain classes of structures, namely: the class of stronglyconnected locally ordered digraphs; the class of connected planar embeddings; and the class of triangulations, with the...
Generalized Hex and logical characterizations of polynomial space
, 1997
"... Finite model theory. Logical characterizations of polynomial space. Completeness via logical reductions. We consider a particular logical characterization of the complexity class PSPACE using firstorder logic, with a builtin successor relation, extended 1 Partially supported by EPSRC Grant GR/ ..."
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Cited by 4 (2 self)
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Finite model theory. Logical characterizations of polynomial space. Completeness via logical reductions. We consider a particular logical characterization of the complexity class PSPACE using firstorder logic, with a builtin successor relation, extended 1 Partially supported by EPSRC Grant GR/K 96564. 2 Most of this work was done whilst the author was visiting the University of Leicester. with an operator corresponding to the wellknown PSPACEcomplete decision problem Generalized Hex; that is, the logic (\SigmaHEX) [FO s ]. It was shown by Makowsky and Pnueli [12] (see also [11]) that any problem in PSPACE can be defined by a sentence of the logic (\SigmaHEX) [FO s ], and, conversely, that any problem definable by a sentence of this logic is in PSPACE. There are numerous other similar
Guarded Quantification in Least Fixed Point Logic
, 2002
"... We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point ..."
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Cited by 2 (1 self)
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We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But guarding quantification increases worstcase time complexity.
Counting proportions of sets: expressive power with almost order. (To appear in
 Latin American Theoretical INformatics, LATIN’06, Lecture Notes in Comp. Sci
, 2005
"... We present a second order logic of proportional quantifiers, , which is essentially a first order language extended with quantifiers that act upon second order variables of a given arity r, and count the fraction of elements in a subset of r– tuples of a model that satisfy a formula. Our logic is ca ..."
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Cited by 1 (1 self)
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We present a second order logic of proportional quantifiers, , which is essentially a first order language extended with quantifiers that act upon second order variables of a given arity r, and count the fraction of elements in a subset of r– tuples of a model that satisfy a formula. Our logic is capable of expressing proportional versions of different problems of complexity up to NPhard, and fragments within our logic capture complexity classes as NL and P, with auxiliary ordering relation. When restricted to monadic second order variables our logic of proportional quantifiers admits a semantic approximation based on almost linear orders, which is not as weak as other known logics with counting quantifiers, for it does not has the bounded number of degrees property. Moreover, we show in this almost ordered setting the existence of an infinite hierarchy inside our monadic language. We extend our inexpressibility result to an almost ordered (not necessarily monadic) fragment of, which in the presence of full order captures P. To obtain all our inexpressibility results we developed combinatorial games appropriate for these logics.
Game Representations of Complexity Classes
 Proc. Eur. Summer School on Logic, Language and Information (European Assoc. Logic, Language and Information
, 2001
"... Many descriptive and computational complexity classes have gametheoretic representations. These can be used to study the relation between different logics and complexity classes in finite model theory. ..."
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Cited by 1 (1 self)
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Many descriptive and computational complexity classes have gametheoretic representations. These can be used to study the relation between different logics and complexity classes in finite model theory.
Logical Definability Versus Computational Complexity: Another Equivalence
"... We dene a class of program schemes, NPSB, as the union of an innite hierarchy of classes of program schemes NPSB(1) NPSB(2) : : :, where our program schemes are built around `highlevel' programming constructs such as arrays, whileloops, assignments, and nondeterminism, and take nite structures ..."
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We dene a class of program schemes, NPSB, as the union of an innite hierarchy of classes of program schemes NPSB(1) NPSB(2) : : :, where our program schemes are built around `highlevel' programming constructs such as arrays, whileloops, assignments, and nondeterminism, and take nite structures as their inputs. Every program scheme of NPSB(i) is actually also a program scheme of an existing class of program schemes NPSA(i), with NPSA dened analogously to NPSB. It has previously been shown that the class of problems accepted by the program schemes of NPSA: is contained in PSPACE; can be realized as the class of problems denable by the sentences of a certain vectorized Lindstrom logic; and has a zeroone law. We prove here that the class of problems accepted by the program schemes of NPSB is contained within the complexity class L NP and can also be realized as the class of problems denable by the sentences of a certain vectorized Lindstrom logic; and we exhibit a problem...
An Infinite Hierarchy in a Class of PolynomialTime Program Schemes
"... We dene a class of program schemes RFDPS constructed around notions of forallloops, repeatloops, arrays and ifthenelse instructions, and which take nite structures as inputs, and we examine the class of problems, denoted RFDPS also, accepted by such program schemes. The class of program schemes ..."
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We dene a class of program schemes RFDPS constructed around notions of forallloops, repeatloops, arrays and ifthenelse instructions, and which take nite structures as inputs, and we examine the class of problems, denoted RFDPS also, accepted by such program schemes. The class of program schemes RFDPS is a logic, in Gurevich's sense, in that: every program scheme accepts an isomorphismclosed class of nite structures; we can recursively check whether a given nite structure is accepted by a given program scheme; and we can recursively enumerate the program schemes of RFDPS. We show that the class of problems RFDPS properly contains the class of problems denable in inductive xedpoint logic (for example, the wellknown problem Parity is in RFDPS) and that there is a strict, innite hierarchy of classes of problems within RFDPS (the union of which is RFDPS) parameterized by the depth of nesting of forallloops in our program schemes. This is the rst strict, innite hierarchy in ...
Program Schemes, Queues, the Recursive Spectrum and ZeroOne Laws
"... We prove that a very basic class of program schemes augmented with access to a queue and an additional numeric universe within which counting is permitted, so that the resulting class is denoted NPSQ+ (1), is such that the class of problems accepted by these program schemes is exactly the class of r ..."
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We prove that a very basic class of program schemes augmented with access to a queue and an additional numeric universe within which counting is permitted, so that the resulting class is denoted NPSQ+ (1), is such that the class of problems accepted by these program schemes is exactly the class of recursively solvable problems. The class of problems accepted by the program schemes of the class NPSQ(1) where only access to a queue, and not the additional numeric universe, is allowed is exactly the class of recursively solvable problems that are closed under extensions. We dene an innite hierarchy of classes of program schemes for which NPSQ(1) is the rst class and the union of the classes of which is the class NPSQ. We show that the class of problems accepted by the program schemes of NPSQ has a zeroone law and is the union of the classes of problems dened by the sentences of all vectorized Lindstrom logics formed using operators whose corresponding problems are recursively solvab...