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Generic trace semantics via coinduction
 Logical Methods in Comp. Sci
, 2007
"... Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace ..."
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Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace
Generic forward and backward simulations
 International Conference on Concurrency Theory (CONCUR 2006), volume 4137 of Lect. Notes Comp. Sci
, 2006
"... Abstract. The technique of forward/backward simulations has been applied successfuly in many distributed and concurrent applications. In this paper, however, we claim that the technique can actually have more genericity and mathematical clarity. We do so by identifying forward/backward simulations a ..."
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Abstract. The technique of forward/backward simulations has been applied successfuly in many distributed and concurrent applications. In this paper, however, we claim that the technique can actually have more genericity and mathematical clarity. We do so by identifying forward/backward simulations as lax/oplax morphisms of coalgebras. Starting from this observation, we present a systematic study of this generic notion of simulations. It is meant to be a generic version of the study by Lynch and Vaandrager, covering both nondeterministic and probabilistic systems. In particular we prove soundness and completeness results with respect to trace inclusion: the proof is by coinduction using the generic theory of traces developed by Jacobs, Sokolova and the author. By suitably instantiating our generic framework, one obtains the appropriate definition of forward/backward simulations for various kinds of systems, for which soundness and completeness come for free. 1
Generic trace theory
 International Workshop on Coalgebraic Methods in Computer Science (CMCS 2006), volume 164 of Elect. Notes in Theor. Comp. Sci
, 2006
"... Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms ..."
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Cited by 14 (5 self)
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Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms of “trace semantics” are instances of a single categorical construction, namely coinduction in a Kleisli category. This claim is based on our main technical result that an initial algebra in
ContextFree Languages, Coalgebraically
, 2011
"... We give a coalgebraic account of contextfree languages using the functor D(X) =2 × X A for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing contextfree grammars as Dcoalgebras; (ii) by defining a format for behavioural differential equations (w.r. ..."
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Cited by 10 (8 self)
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We give a coalgebraic account of contextfree languages using the functor D(X) =2 × X A for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing contextfree grammars as Dcoalgebras; (ii) by defining a format for behavioural differential equations (w.r.t. D) for which the unique solutions are precisely the contextfree languages; and (iii) as the Dcoalgebra of generalized regular expressions in which the Kleene star is replaced by a unique fixed point operator. In all cases, semantics is defined by the unique homomorphism into the final coalgebra of all languages, paving the way for coinductive proofs of contextfree language equivalence. Furthermore, the three characterizations can serve as the basis for the definition of a general coalgebraic notion of contextfreeness, which we see as the ultimate longterm goal of the present study.
Coalgebraic trace semantics for probabilistic systems, 2005
 In preparation
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Coalgebraic characterizations of contextfree languages
 Logical Methods in Computer Science
"... Abstract. In this article, we provide three coalgebraic characterizations of the class of contextfree languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying outputderivative pairs. Final coalgebra semantics then gives an interpretation fu ..."
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Abstract. In this article, we provide three coalgebraic characterizations of the class of contextfree languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying outputderivative pairs. Final coalgebra semantics then gives an interpretation function into the final coalgebra of all languages with the usual output and derivative operations. The first characterization is based on systems, where each derivative is given as a finite language over the set of nonterminals; the second characterization on systems where derivatives are given as elements of a termalgebra; and the third characterization is based on adding coalgebraic structure to a class of closed (unique) fixed point expressions. We prove equivalences between these characterizations, discuss the generalization from languages to formal power series, as well as the relationship to the generalized powerset construction. 1.
Stream Differential Equations: Specification Formats and Solution Methods
, 2014
"... Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been dev ..."
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Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades. In this paper we present a survey of the many results in this area. Our focus is on the classification of different formats of stream differential equations, their solution methods, and the classes of streams they can define. Moreover, we describe in detail the connection between the socalled syntactic solution method and abstract GSOS.
SEMANTICS OF GRAMMARS AND ATTRIBUTES VIA INITIALITY
"... ABSTRACT. This paper uses elementary categorical techniques to systematically describe the semantics of contextfree grammars and of attribute evaluation for such grammars. The novelty lies in capturing inherited attributes and their evaluation via exponents and naturality. 1. ..."
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ABSTRACT. This paper uses elementary categorical techniques to systematically describe the semantics of contextfree grammars and of attribute evaluation for such grammars. The novelty lies in capturing inherited attributes and their evaluation via exponents and naturality. 1.
Traces, Executions and Schedulers,
"... Abstract. A theory of traces of computations has emerged within the field of coalgebra, via finality in Kleisli categories. In concurrency theory, traces are traditionally obtained from executions, by projecting away states. These traces and executions are sequences and will be called “thin”. The co ..."
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Abstract. A theory of traces of computations has emerged within the field of coalgebra, via finality in Kleisli categories. In concurrency theory, traces are traditionally obtained from executions, by projecting away states. These traces and executions are sequences and will be called “thin”. The coalgebraic approach gives rise to both “thin ” and “fat” traces/executions, where in the “fat ” case the structure of computations is preserved. This distinction between thin and fat will be introduced first. It is needed for a theory of schedulers in a coalgebraic setting, of which we only present the very basic definitions and results. 1