### A Coalgebraic Perspective on Minimization and Determinization ⋆

"... Abstract. Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we ..."

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Abstract. Coalgebra offers a unified theory of state based systems, including infinite streams, labelled transition systems and deterministic automata. In this procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization. First, we show that for coalgebras in categories equipped with factorization structures, there exists an abstract procedure for equivalence checking. Then, we consider coalgebras in categories without suitable factorization structures: under certain conditions, it is possible to apply the above procedure after transforming coalgebras with reflections. This transformation can be thought of as some kind of determinization. We will apply our theory to the following examples: conditional transition systems and (non-deterministic) automata. 1

### MFPS 2009 Categories of Timed Stochastic Relations

"... Stochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus ha ..."

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Stochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior. These languages essentially denote continuous-time stochastic processes, obtained through an operational semantics in a probabilistic transition system. In this paper we seek a more descriptive foundation for the semantics of stochastic behavior using categories and monads. We model a first-order imperative language with stochastic delay by identifying probabilistic choice and delay as separate effects, modeling each with a monad, and combining the monads to build a model for the stochastic language.

### Fusion of Monadic (Co)Recursive Programs

"... this paper we present the definitions and some fusion laws corresponding to monadic anamorphism and monadic hylomorphism. We also give a brief account of some nontrivial applications that can be represented in terms of these functionals. (A detailed treatment of the topics presented in this paper ca ..."

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this paper we present the definitions and some fusion laws corresponding to monadic anamorphism and monadic hylomorphism. We also give a brief account of some nontrivial applications that can be represented in terms of these functionals. (A detailed treatment of the topics presented in this paper can be found in [17].) 2 Preliminaries

### Abstract A Coalgebraic Foundation for Linear Time Semantics

"... We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for non-deterministic choice. In Set, this gives a category with ordinary transition systems as objects and with morphisms characterised i ..."

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We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for non-deterministic choice. In Set, this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical abstract model for trace equivalence and can be obtained by extending the final coalgebra of the deterministic action behaviour to the Kleisli category of the non-empty powerset monad. The corresponding final coalgebra semantics is fully abstract with respect to trace equivalence.

### GENERIC TRACE SEMANTICS VIA COINDUCTION ∗

, 2007

"... Vol. 3 (4:11) 2007, pp. 1–36 www.lmcs-online.org ..."

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### found at the ENTCS Macro Home Page.

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