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39
PSPACE bounds for rank 1 modal logics
 IN LICS’06
, 2006
"... For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank1 logics enjoy a sh ..."
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Cited by 36 (19 self)
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For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank1 logics enjoy a shallow model property and thus are, under mild assumptions on the format of their axiomatisation, in PSPACE. This leads to a unified derivation of tight PSPACEbounds for a number of logics including K, KD, coalition logic, graded modal logic, majority logic, and probabilistic modal logic. Our generic algorithm moreover finds tableau proofs that witness pleasant prooftheoretic properties including a weak subformula property. This generality is made possible by a coalgebraic semantics, which conveniently abstracts from the details of a given model class and thus allows covering a broad range of logics in a uniform way.
A Finite Model Construction For Coalgebraic Modal Logic
"... In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness result ..."
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Cited by 35 (17 self)
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In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal logic admits a complete axiomatization of rank 1; it also enables us to establish a generic decidability result and a first complexity bound. Examples covered by these general results include, besides standard HennessyMilner logic, graded modal logic and probabilistic modal logic.
Towards Weak Bisimulation For Coalgebras
, 2002
"... This report contains a novel approach to observation equivalence for coalgebras. ..."
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Cited by 11 (1 self)
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This report contains a novel approach to observation equivalence for coalgebras.
Coalgebras For Binary Methods: Properties Of Bisimulations And Invariants
, 2001
"... Coalgebras for endofunctors C > C can be used to model classes of objectoriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This ext ..."
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Cited by 10 (4 self)
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Coalgebras for endofunctors C > C can be used to model classes of objectoriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors C^op x C > C . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard results.
From Algebras and Coalgebras to Dialgebras
, 2001
"... This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras. ..."
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Cited by 10 (0 self)
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This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras.
Dialgebraic Specification and Modeling
"... corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube ..."
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Cited by 4 (4 self)
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corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube
Greatest Bisimulations for Binary Methods
 IN PROCEEDINGS OF CMCS’02, VOLUME 65(1) OF ENTCS
, 2002
"... ..."
Predicate and Relation Lifting for Parametric Algebraic Specifications
 CMCS'04
, 2004
"... Relation lifting [6] extends an endofunctor F: C C to a functor Rel(F): Rel(C) Rel(C), where Rel(C) is a suitable category of relations over C. The relation lifting for the functor F can be used to define the notion of bisimulation for coalgebras X F (X). The related notion of predicate lifting can ..."
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Cited by 2 (0 self)
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Relation lifting [6] extends an endofunctor F: C C to a functor Rel(F): Rel(C) Rel(C), where Rel(C) is a suitable category of relations over C. The relation lifting for the functor F can be used to define the notion of bisimulation for coalgebras X F (X). The related notion of predicate lifting can be used to define invariants for Fcoalgebras. Predicate and relation lifting can be directly defined for a rich class of polynomial functors [5,6,19]. In this paper I investigate the case where the functor F is defined as the initial semantics of a (single sorted) parametric algebraic specification.
Imperative Objectbased Calculi In (Co)Inductive Type Theories
 In Barendregt and Nipkow [2
, 2003
"... We discuss the formalization of Abadi and Cardelli's imp#, a paradigmatic objectbased calculus with types and side e#ects, in (Co)Inductive Type Theories. ..."
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Cited by 2 (0 self)
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We discuss the formalization of Abadi and Cardelli's imp#, a paradigmatic objectbased calculus with types and side e#ects, in (Co)Inductive Type Theories.
Coinductive Verification of Program Optimizations using Similarity Relations
"... Formal verification methods have gained increased importance due to their ability to guarantee system correctness and improve reliability. Nevertheless, the question how proofs are to be formalized in theorem provers is far from being trivial, yet very important as one needs to spend much more time ..."
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Formal verification methods have gained increased importance due to their ability to guarantee system correctness and improve reliability. Nevertheless, the question how proofs are to be formalized in theorem provers is far from being trivial, yet very important as one needs to spend much more time on verification if the formalization was not cleverly chosen. In this paper, we develop and compare two different possibilities to express coinductive proofs in the theorem prover Isabelle/HOL. Coinduction is a proof method that allows for the verification of properties of also nonterminating statetransition systems. Since coinduction is not as widely used as other proof techniques as e.g. induction, there are much fewer “recipes ” available how to formalize corresponding proofs and there are also fewer proof strategies implemented in theorem provers for coinduction. In this paper, we investigate formalizations for coinductive proofs of properties on state transition sequences. In particular, we compare two different possibilities for their formalization and show their equivalence. The first of these two formalizations captures the mathematical intuition, while the second can be used more easily in a theorem prover. We have formally verified the equivalence of these criteria in Isabelle/HOL, thus establishing a coalgebraic verification framework. To demonstrate that our verification framework is suitable for the verification of compiler optimizations, we have introduced three different, rather simple transformations that capture typical problems in the verification of optimizing compilers, even for nonterminating source programs.