{"title":"Context Matching for Compressed Terms","authors":"Adrià Gascón, Guillem Godoy, M. Schmidt-Schauß","doi":"10.1109/LICS.2008.17","DOIUrl":"https://doi.org/10.1109/LICS.2008.17","url":null,"abstract":"This paper is an investigation of the matching problem for term equations s = t where s contains context variables and first-order variables, and both terms s and t are given using some kind of compressed representation. The main result is a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. NP-completeness is obtained when the terms are represented using the more general formalism of singleton tree grammars. As an ingredient of this proof, we also show that the special case of first-order matching with singleton tree grammars is decidable in polynomial time.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126877910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Axiomatic Derivation of Absolute Lower Bounds","authors":"Y. Moschovakis","doi":"10.1109/LICS.2008.52","DOIUrl":"https://doi.org/10.1109/LICS.2008.52","url":null,"abstract":"The ancient Euclidean algorithm computes the greatest common divisor gcd(m, n) of two natural numbers from (or relative to) the remainder operation rem, which is assumed as primitive; it requires no more than 2 log(min(m, n)) applications of the remainder operation to compute gcd(m, n) (for m, n ges 2), and it is not known to be optimal: Conjecture: for every algorithm a which computes on Nopf from rem the greatest common divisor function, there is a constant r > 0 such that for infinitely many pairs a ges b ges 1, calpha(a, b) ges rlog2(a), where calpha(m,n) counts the number of calls to \"the remainder oracle\" required by a for the computation of gcd(m, n). The conjecture claims a logarithmic lower bound for all algorithms which compute gcd(m, n) from the remainder operation, not just those expressed by a specific class of computation models. In this lecture the author develops an approach to the theory of algorithms in the style of abstract model theory which makes it possible to make precise and (on occasion) prove the existence of non-trivial, absolute lower bounds for a wide variety of problems and specified primitives, including many of the results in the bibliography.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130811576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Algebraic Process Calculus","authors":"E. Beffara","doi":"10.1109/LICS.2008.40","DOIUrl":"https://doi.org/10.1109/LICS.2008.40","url":null,"abstract":"We present an extension of the piI-calculus with formal sums of terms. A study of the properties of this sum reveals that its neutral element can be used to make assumptions about the behaviour of the environment of a process. Furthermore, the formal sum appears as a fundamental construct that can be used to decompose both internal and external choice. From these observations, we derive an enriched calculus that enjoys a confluent reduction which preserves the testing semantics of processes. This system is shown to be strongly normalising for terms without replication, and the study of its normal forms provides fully abstract trace semantics for testing of piI processes.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117223194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Caterpillar Duality for Constraint Satisfaction Problems","authors":"C. Carvalho, V. Dalmau, A. Krokhin","doi":"10.1109/LICS.2008.19","DOIUrl":"https://doi.org/10.1109/LICS.2008.19","url":null,"abstract":"The study of constraint satisfaction problems definable in various fragments of Datalog has recently gained considerable importance. We consider constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog - monadic linear Datalog with at most one EDB per rule. We give combinatorial and algebraic characterisations of such problems, in terms of caterpillar dualities and lattice operations, respectively. We then apply our results to study graph H-colouring problems.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134634956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Logical Characterization of Individual-Based Models","authors":"J. Lynch","doi":"10.1109/LICS.2008.27","DOIUrl":"https://doi.org/10.1109/LICS.2008.27","url":null,"abstract":"Individual-based models are a relatively new approach to modelling dynamical systems of interacting entities, for example molecules in a biological cell. Although they are computationally expensive, they have the capability of modelling systems more realistically than traditional state-variable models. We give a formal definition of individual-based models, which includes state-variable models as a special case. We examine the questions of when state-variable models are sufficient for accurate modelling of a system, and when individual-based models are necessary. We define notions of abstraction and approximation, and give sufficient conditions that imply that an individual-based model can be approximated by a deterministic state-variable model. We also give negative results: examples of individual-based models that cannot be approximated by any state-variable model.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133393021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maltsev + Datalog --≫ Symmetric Datalog","authors":"Víctor Dalmau, Benoît Larose","doi":"10.1109/LICS.2008.14","DOIUrl":"https://doi.org/10.1109/LICS.2008.14","url":null,"abstract":"Let B be a finite, core relational structure and let A be the algebra associated to B, i.e. whose terms are the operations on the universe of B that preserve the relations of B. We show that if A generates a so-called arithmetical variety then CSP(B), the constraint satisfaction problem associated to B, is solvable in Logspace; in fact notCSP(B) is expressible in symmetric Datalog. In particular, we obtain that notCSP(B) is expressible in Datalog and the relations of B are invariant under a Maltsev operation then notCSP(B) is in symmetric Datalog.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127983183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"From Axioms to Analytic Rules in Nonclassical Logics","authors":"A. Ciabattoni, Nikolaos Galatos, K. Terui","doi":"10.1109/LICS.2008.39","DOIUrl":"https://doi.org/10.1109/LICS.2008.39","url":null,"abstract":"We introduce a systematic procedure to transform large classes of (Hilbert) axioms into equivalent inference rules in sequent and hypersequent calculi. This allows for the automated generation of analytic calculi for a wide range of prepositional nonclassical logics including intermediate, fuzzy and substructural logics. Our work encompasses many existing results, allows for the definition of new calculi and contains a uniform semantic proof of cut-elimination for hypersequent calculi.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114415417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Asymptotic Nullstellensatz and Polynomial Calculus Proof Complexity","authors":"Søren Riis","doi":"10.1109/LICS.2008.30","DOIUrl":"https://doi.org/10.1109/LICS.2008.30","url":null,"abstract":"We show that the asymptotic complexity of uniformly generated (expressible in first-order (FO) logic) prepositional tautologies for the nullstellensatz proof system (NS) as well as for polynomial calculus, (PC) has four distinct types of asymptotic behavior over fields of finite characteristic. More precisely, based on some highly non-trivial work by Krajicek, we show that for each prime p there exists a function l(n) G isin Omega(log(n)) for NS and l(n) G Omega (log(log(n)) for PC, such that the prepositional translation of any FO formula (that fails in all finite models), has degree proof complexity over fields of characteristic p, that behave in 4 mutually distinct ways: (i) The degree complexity is bound by a constant. (ii) The degree complexity is at least l(n) for all values of n. (iii) The degree complexity is at least l(n) except in a finite number of regular subsequences of infinite size, where the degree is constant. (iv) The degree complexity fluctuates in a very particular way with the degree complexity taking different constant values on an infinite number of regular subsequences each of infinite size. We leave it as an open question whether the classification remains valid for l[n) isin nOmega(1) or even for I (n) isin Omega(n). Finally, we show that for any non-empty proper subset A sube {(i), (ii), (iii), (iv)} the decision problem of whether a given input FO formula Psi has type belonging to A - is undecidable.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124380139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hypergraph Acyclicity and Extension Preservation Theorems","authors":"David Duris","doi":"10.1109/LICS.2008.12","DOIUrl":"https://doi.org/10.1109/LICS.2008.12","url":null,"abstract":"A class of structures satisfies the extension preservation theorem if, on this class, every first order sentence is preserved under extension iff it is equivalent to an existential sentence. We consider different acyclicity notions for hypergraphs (gamma, beta and alpha-acyclicity and also acyclicity on hypergraph quotients) and estimate their influence on the validity of the extension preservation theorem on classes of finite structures. More precisely, we prove that gamma-acyclic classes satisfy the extension preservation theorem, whereas beta-acyclic classes do not. We also extend the validity of the extension preservation theorem for a generalization of gamma-acyclicity that we call gamma-acyclic k-quotient. To achieve this, we make a reduction from finite structures to their k-quotients and we use combinatorial arguments on gamma-acyclic hypergraphs.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"45 16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132136813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Focusing on Binding and Computation","authors":"Daniel R. Licata, N. Zeilberger, R. Harper","doi":"10.1109/LICS.2008.48","DOIUrl":"https://doi.org/10.1109/LICS.2008.48","url":null,"abstract":"Variable binding is a prevalent feature of the syntax and proof theory of many logical systems. In this paper, we define a programming language that provides intrinsic support for both representing and computing with binding. This language is extracted as the Curry-Howard interpretation of a focused sequent calculus with two kinds of implication, of opposite polarity. The representational arrow extends systems of definitional reflection with a notion of scoped inference rules, which are used to represent binding. On the other hand, the usual computational arrow classifies recursive functions defined by pattern-matching. Unlike many previous approaches, both kinds of implication are connectives in a single logic, which serves as a rich logical framework capable of representing inference rules that mix binding and computation.","PeriodicalId":298300,"journal":{"name":"2008 23rd Annual IEEE Symposium on Logic in Computer Science","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115422087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}