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Playing with Boolean blocks, part I: Post’s lattice with applications to complexity theory
 SIGACT News
"... Let us imagine children playing with a box containing a large number of building blocks such as LEGO TM, fischertechnik ® , Polydron, or something similar. Each block belongs to a certain class (given by, e. g., color, shape, or size) and usually the number of different such classes is relatively sm ..."
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Cited by 45 (13 self)
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Let us imagine children playing with a box containing a large number of building blocks such as LEGO TM, fischertechnik ® , Polydron, or something similar. Each block belongs to a certain class (given by, e. g., color, shape, or size) and usually the number of different such classes is relatively small. It is amazing to see how involved the constructions are that can be built by the kids. From
Ontologies and databases: The DLLite approach
 In Reasoning Web, volume 5689 of LNCS
, 2009
"... Abstract. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual vie ..."
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Cited by 26 (17 self)
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Abstract. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual view over data repositories is becoming more and more popular, but for it to become widespread in standard applications, it is fundamental that the conceptual layer through which the underlying data layer is accessed does not introduce a significant overhead in dealing with the data. Based on these observations, in recent years a family of DLs, called DLLite, has been proposed, which is specifically tailored to capture basic ontology and conceptual data modeling languages, while keeping low complexity of reasoning and of answering complex queries, in particular when the complexity is measured w.r.t. the size of the data. In this article, we present a detailed account of the major results that have been achieved for the DLLite family. Specifically, we concentrate on DLLiteA,id, an expressive member of this family, present algorithms for reasoning and query answering over DLLiteA,id ontologies,
The Complexity of Satisfiability Problems: Refining Schaefer’s Theorem
 J. Comput. Sys. Sci
"... problem for a given constraint language is either in P or is NPcomplete, and identified all tractable cases. Schaefer’s dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomialtime isomorphism (and these isomorphism types are distinct if and onl ..."
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Cited by 17 (7 self)
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problem for a given constraint language is either in P or is NPcomplete, and identified all tractable cases. Schaefer’s dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomialtime isomorphism (and these isomorphism types are distinct if and only if P ̸ = NP). We show that if one considers AC 0 isomorphisms, then there are exactly six isomorphism types (assuming that the complexity classes NP, P, ⊕L, NL, and L are all distinct). A similar classification holds for quantified constraint satisfaction problems.
The Descriptive Complexity Approach to LOGCFL
, 1998
"... Building upon the known generalizedquantifierbased firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory ..."
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Cited by 11 (5 self)
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Building upon the known generalizedquantifierbased firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the contextfree languages, and we obtain the surprising result that a variant of Greibach's "hardest contextfree language" is LOGCFLcomplete under quantifierfree BITfree projections. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that firstorder logic with majority of pairs is strictly more expressive than firstorder with major...
Evaluating monotone circuits on cylinders, planes, and torii
 In Proc. 23rd Symposium on Theoretical Aspects of Computing (STACS), Lecture Notes in Computer Science
, 2006
"... Abstract. We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC 3 in general, and in LogDCFL for the special case of upward stratified circuits. We characterize cylindricality, which is stronger than planarity but strict ..."
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Cited by 10 (2 self)
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Abstract. We revisit monotone planar circuits MPCVP, with special attention to circuits with cylindrical embeddings. MPCVP is known to be in NC 3 in general, and in LogDCFL for the special case of upward stratified circuits. We characterize cylindricality, which is stronger than planarity but strictly generalizes upward planarity, and make the characterization partially constructive. We use this construction, and four key reduction lemmas, to obtain several improvements. We show that monotone circuits with embeddings that are stratified cylindrical, cylindrical, planar oneinputface and focused can be evaluated in LogDCFL, AC 1 (LogDCFL), LogCFL and AC 1 (LogDCFL) respectively. We note that the NC 3 algorithm for general MPCVP is in AC 1 (LogCFL) =SAC 2.Finally, we show that monotone circuits with toroidal embeddings can, given such an embedding, be evaluated in NC. 1
Zandron: Simulating the Fredkin Gate with Energy–based P Systems, in the present volume
"... Abstract. Reversibility plays a fundamental role when the possibility to perform computations with minimal energy dissipation is considered. Many papers on reversible computation have appeared in literature: the most famous are certainly the work of Bennett on (universal) reversible Turing machines ..."
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Cited by 8 (4 self)
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Abstract. Reversibility plays a fundamental role when the possibility to perform computations with minimal energy dissipation is considered. Many papers on reversible computation have appeared in literature: the most famous are certainly the work of Bennett on (universal) reversible Turing machines and the work of Fredkin and Toffoli on conservative logic. The latter is based upon the Fredkin gate, a reversible and “conservative ” (according to a definition given by Fredkin and Toffoli) three–input/three–output boolean gate. In this paper we introduce energy–based P systems as a parallel and distributed model of computation in which the amount of energy manipulated and/or consumed during computations is taken into account. Moreover, we show how energy–based P systems can be used to simulate the Fredkin gate. The proposed P systems that perform the simulation turn out to be themselves reversible and conservative. 1
Logic meets algebra: the case of regular languages
 Logical Methods in Computer Science
"... Abstract. The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Büchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point ..."
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Cited by 8 (1 self)
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Abstract. The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Büchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point of view on automata is an essential complement of this classification: by providing alternative, algebraic characterizations for the classes, it often yields the only opportunity for the design of algorithms that decide expressibility in some logical fragment. We survey the existing results relating the expressibility of regular languages in logical fragments of MSO[S] with algebraic properties of their minimal automata. In particular, we show that many of the best known results in this area share the same underlying mechanics and rely on a very strong relation between logical substitutions and blockproducts of pseudovarieties of monoid. We also explain the impact of these connections on circuit complexity theory. 1.
Semantics of FODA feature diagrams
 Proceedings SPLC 2004 Workshop on Software Variability Management for Product Derivation – Towards Tool Support
, 2004
"... Abstract. Extended Feature Oriented Domain Analysis (FODA) Feature Diagrams (EFD) were introduced to compensate for a purported ambiguity and lack of precision and expressiveness of the original FODA feature diagrams (OFD). However, EFD never received a formal semantics, which is the hallmark of pre ..."
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Cited by 7 (3 self)
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Abstract. Extended Feature Oriented Domain Analysis (FODA) Feature Diagrams (EFD) were introduced to compensate for a purported ambiguity and lack of precision and expressiveness of the original FODA feature diagrams (OFD). However, EFD never received a formal semantics, which is the hallmark of precision and unambiguity. We propose here a semantics for both diagrams. From this we demonstrate that OFD are precise, unambiguous, and expressively complete, and thus that all extensions add no expressiveness. A finer notion is thus needed to compare these languages. Two solutions are wellestablished: succinctness and embeddability, that measures naturalness of a language. This tool shows that EFD indeed bring some naturalness, but are harmfully redundant and that the same naturalness can be attained with the simpler varied FD (VFD). We also show that no ambiguity is present, in fact.
Computational Complexity of an Optical Model of Computation
, 2005
"... We investigate the computational complexity of an optically inspired model of computation. The model is called the continuous space machine and operates in discrete timesteps over a number of twodimensional complexvalued images of constant size and arbitrary spatial resolution. We define a number ..."
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Cited by 7 (7 self)
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We investigate the computational complexity of an optically inspired model of computation. The model is called the continuous space machine and operates in discrete timesteps over a number of twodimensional complexvalued images of constant size and arbitrary spatial resolution. We define a number of optically inspired complexity measures and data representations for the model. We show the growth of each complexity measure under each of the model's operations. We characterise the power of an important discrete restriction of the model. Parallel time on this variant of the model is shown to correspond, within a polynomial, to sequential space on Turing machines, thus verifying the parallel computation thesis. We also give a characterisation of the class NC. As a result the model has computational power equivalent to that of many wellknown parallel models. These characterisations give a method to translate parallel algorithms to optical algorithms and facilitate the application of the complexity theory toolbox to optical computers. Finally we show that another variation on the model is very powerful;