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Lohrey Markus - One of the best experts on this subject based on the ideXlab platform.
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The First-Order Theory of Ground Tree Rewrite Graphs
2014Co-Authors: Göller Stefan, Lohrey MarkusAbstract:We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single Unary Predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.Comment: accepted for Logical Methods in Computer Scienc
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the first order theory of ground tree rewrite graphs
2011Co-Authors: Lohrey MarkusAbstract:We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single Unary Predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.
Markus Lohrey - One of the best experts on this subject based on the ideXlab platform.
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the complexity of the first order theory of ground tree rewrite graphs
2014Co-Authors: Stefan Göller, Markus LohreyAbstract:The uniform first-order theory of ground tree rewrite graphs is the set of all pairs consisting of a ground tree rewrite system and a first-order sentence that holds in the graph defined by the ground tree rewrite system. We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2 poly(n) , O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2 poly(n) , poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single Unary Predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.
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The First-Order Theory of Ground Tree Rewrite Graphs
2014Co-Authors: Stefan Göller, Markus LohreyAbstract:We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(22poly(n) , O(n)). Providing a matching lower bound, we show that there is a fixed ground tree rewrite graph whose first-order theory is hard for ATIME(22poly(n) , poly(n)) with respect to logspace reductions. Finally, we prove that there is a fixed ground tree rewrite graph together with a single Unary Predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory. For a long version of this paper with complete proofs see [11]
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The first-order theory of ground tree rewrite graphs. arXiv.org
2011Co-Authors: Markus LohreyAbstract:ABSTRACT. We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(22 poly(n), O(n)). Providing a matching lower bound, we show that there is a fixed ground tree rewrite graph whose first-order theory is hard for ATIME(22 poly(n), poly(n)) with respect to logspace reductions. Finally, we prove that there is a fixed ground tree rewrite graph together with a single Unary Predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory. For a long version of this paper with complete proofs see [11].
Alexander Rabinovich - One of the best experts on this subject based on the ideXlab platform.
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Decidable Extensions of Church’s Problem
2010Co-Authors: Alexander RabinovichAbstract:Abstract. For a two-variable formula B(X,Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of a finite-state operator Y=F(X) such that B(X,F(X)) is universally valid over Nat. Büchi and Landweber (1969) proved that the Church synthesis problem is decidable. We investigate a parameterized version of the Church synthesis problem. In this extended version a formula B and a finite-state operator F might contain as a parameter a Unary Predicate P. A large class of Predicates P is exhibited such that the Church problem with the parameter P is decidable. Our proofs use Composition Method and game theoretical techniques.
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Church Synthesis Problem with Parameters
2009Co-Authors: Alexander RabinovichAbstract:Abstract. For a two-variable formula ψ(X, Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of an operator Y = F(X) such that ψ(X, F(X)) is universally valid over Nat. Büchi and Landweber proved that the Church synthesis problem is decidable; moreover, they showed that if there is an operator F that solves the Church Synthesis Problem, then it can also be solved by an operator defined by a finite state automaton or equivalently by an MLO formula. We investigate a parameterized version of the Church synthesis problem. In this version ψ might contain as a parameter a Unary Predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of 〈Nat, <, P 〉 is decidable. We prove that the Büchi-Landweber theorem can be extended only to ultimately periodic parameters. However, the MLO-definability part of the Büchi-Landweber theorem holds for the parameterized version of the Church synthesis problem. 1
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Definability in Rationals with Real Order in the Background
2007Co-Authors: Yuri Gurevich, Alexander Rabinovich, Er RabinovichAbstract:The paper deals with logically definable families of sets (or point-sets) of rational numbers. In particular we are interested whether the families definable over the real line with a Unary Predicate for the rationals are definable over the rational order alone. Let #(X, Y ) and #(Y ) range over formulas in the first-order monadic language of order. Let Q be the set of rationals and F be the family of subsets J of Q such that #(Q, J) holds over the real line. The question arises whether, for every #, F can be defined by means of an appropriate #(Y ) interpreted over the rational order. We answer the question negatively. The answer remains negative if the firstorder logic is strengthen to weak monadic second-order logic. The answer is positive for the restricted version of monadic second-order logic where set quantifiers range over open sets. The case of full monadic second-order logic remains open. 1 Introduction We consider the monadic second-order theory of linear order. For the s..
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The Church Synthesis Problem with Parameters
2007Co-Authors: Alexander RabinovichAbstract:For a two-variable formula ψ(X,Y) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of an operator Y=F(X) such that ψ(X,F(X)) is universally valid over Nat. B\"{u}chi and Landweber proved that the Church synthesis problem is decidable; moreover, they showed that if there is an operator F that solves the Church Synthesis Problem, then it can also be solved by an operator defined by a finite state automaton or equivalently by an MLO formula. We investigate a parameterized version of the Church synthesis problem. In this version ψ might contain as a parameter a Unary Predicate P. We show that the Church synthesis problem for P is computable if and only if the monadic theory of is decidable. We prove that the B\"{u}chi-Landweber theorem can be extended only to ultimately periodic parameters. However, the MLO-definability part of the B\"{u}chi-Landweber theorem holds for the parameterized version of the Church synthesis problem.
Fausto Giunchiglia - One of the best experts on this subject based on the ideXlab platform.
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A Local Models Semantics for Propositional Attitudes
2000Co-Authors: Fausto Giunchiglia, Chiara GhidiniAbstract:Our starting point is a formulation of modal logics, described in previous papers, defined in terms of a hierarchy of distinct (that is, not amalgamated) metatheories. These logics, called Hierarchical Multilanguage Belief (HMB) systems formalize the current practice in the implementation of propositional attitudes, and in particular belief, inside complex reasoning systems. Our goal is to define e new semantics for HMB systems, called local models semantics, which captures their underlying intuitions. In local models semantics each (meta)theory defines a set of first order models, called ‘local models’; belief is a Unary Predicate; and the extension of the belief Predicate is computed by enforcing constraints among sets of local model
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A Local Models Semantics for Propositional Attitudes
1997Co-Authors: Fausto Giunchiglia, Ghidini C, Chiara GhidiniAbstract:Our starting point is a formulation of modal logics, described in previous papers, defined in terms of a hierarchy of distinct (that is, not amalgamated) metatheories. These logics, called Hierarchical Multilanguage Belief (HMB) systems formalize the current practice in the implementation of propositional attitudes, and in particular belief, inside complex reasoning systems. Our goal is to define a new semantics for HMB systems, called local models semantics, which captures their underlying intuitions. In local models semantics each (meta)theory defines a set of first order models, called "local models"; belief is a Unary Predicate; and the extension of the belief Predicate is computed by enforcing constraints among sets of local models. 1 Introduction We are interested in the representation and mechanization of propositional attitudes, and belief in particular, inside complex reasoning programs, e.g. knowledge representation systems, natural language understanding systems, or multiag..
Chiara Ghidini - One of the best experts on this subject based on the ideXlab platform.
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A Local Models Semantics for Propositional Attitudes
2000Co-Authors: Fausto Giunchiglia, Chiara GhidiniAbstract:Our starting point is a formulation of modal logics, described in previous papers, defined in terms of a hierarchy of distinct (that is, not amalgamated) metatheories. These logics, called Hierarchical Multilanguage Belief (HMB) systems formalize the current practice in the implementation of propositional attitudes, and in particular belief, inside complex reasoning systems. Our goal is to define e new semantics for HMB systems, called local models semantics, which captures their underlying intuitions. In local models semantics each (meta)theory defines a set of first order models, called ‘local models’; belief is a Unary Predicate; and the extension of the belief Predicate is computed by enforcing constraints among sets of local model
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A Local Models Semantics for Propositional Attitudes
1997Co-Authors: Fausto Giunchiglia, Ghidini C, Chiara GhidiniAbstract:Our starting point is a formulation of modal logics, described in previous papers, defined in terms of a hierarchy of distinct (that is, not amalgamated) metatheories. These logics, called Hierarchical Multilanguage Belief (HMB) systems formalize the current practice in the implementation of propositional attitudes, and in particular belief, inside complex reasoning systems. Our goal is to define a new semantics for HMB systems, called local models semantics, which captures their underlying intuitions. In local models semantics each (meta)theory defines a set of first order models, called "local models"; belief is a Unary Predicate; and the extension of the belief Predicate is computed by enforcing constraints among sets of local models. 1 Introduction We are interested in the representation and mechanization of propositional attitudes, and belief in particular, inside complex reasoning programs, e.g. knowledge representation systems, natural language understanding systems, or multiag..