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Rewriting On Cyclic Structures: Equivalence Between The Operational And The Categorical Description
, 1999
"... . We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, fo ..."
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Cited by 14 (7 self)
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. We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures, and to relate term graph rewriting to other rewriting formalisms. R'esum'e. Nous pr'esentons une formulation cat'egorique de la r'e'ecriture des graphes cycliques des termes, bas'ee sur une variante de 2theorie alg'ebrique. Nous prouvons que cette pr'esentation est 'equivalente `a la d'efinition op'erationnelle propos'ee par Barendregt et d'autres auteurs, mais pas dons le cas des radicaux circulaires, pour lesquels nous proposons (et justifions formellem...
Duality for Labelled Markov Processes
"... Labelled Markov processes (LMPs) are automata whose transitions are given by probability distributions. In this paper we present a `universal' LMP as the spectrum of a commutative C # algebra consisting of formal linear combinations of labelled trees. We characterize the state space of the ..."
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Labelled Markov processes (LMPs) are automata whose transitions are given by probability distributions. In this paper we present a `universal' LMP as the spectrum of a commutative C # algebra consisting of formal linear combinations of labelled trees. We characterize the state space of the universal LMP as the set of homomorphims from an ordered commutative monoid of labelled trees into the multiplicative unit interval. This yields a simple semantics for LMPs which is fully abstract with respect to probabilistic bisimilarity. We also consider LMPs with entry points and exit points in the setting of iteration theories. We define an iteration theory of LMPs by specifying its categorical dual: a certain category of C*algebras. We find that the basic operations for composing LMPs have simple definitions in the dual category.
Value Recursion in Monadic Computations
 OGI School of Science and Engineering, OHSU
, 2002
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An extension theorem with an application to formal tree series
 BRICS Report Series
, 2002
"... series ..."
Kleene Algebra with Products and Iteration Theories
"... We develop a typed equational system that subsumes both iteration theories and typed Kleene algebra in a common framework. Our approach is based on cartesian categories endowed with commutative strong monads to handle nondeterminism. ..."
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Cited by 1 (1 self)
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We develop a typed equational system that subsumes both iteration theories and typed Kleene algebra in a common framework. Our approach is based on cartesian categories endowed with commutative strong monads to handle nondeterminism.
Typed Kleene Algebra with Products and Iteration Theories
"... Abstract—We develop a typed equational system that subsumes both iteration theories and typed Kleene algebra in a common framework. Our approach is based on cartesian categories endowed with commutative strong monads to handle nondeterminism. I. ..."
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Abstract—We develop a typed equational system that subsumes both iteration theories and typed Kleene algebra in a common framework. Our approach is based on cartesian categories endowed with commutative strong monads to handle nondeterminism. I.
A note on Coinduction and Weak Bisimilarity for While Programs
 Theoretical Informatics and Applications (RAIRO
, 1998
"... An illustration of coinduction in terms of a notion of weak bisimilarity is presented. First, an operational semantics O for while programs is defined in terms of a final automaton. It identifies any two programs that are weakly bisimilar, and induces in a canonical manner a compositional model D ..."
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An illustration of coinduction in terms of a notion of weak bisimilarity is presented. First, an operational semantics O for while programs is defined in terms of a final automaton. It identifies any two programs that are weakly bisimilar, and induces in a canonical manner a compositional model D. Next O = D is proved by coinduction. 1991 Mathematics Subject Classification: 68Q10, 68Q55 1991 Computing Reviews Classification System: D.3, F.1, F.3 Keywords & Phrases: Coalgebra, automaton, weak bisimulation, coinduction, while program 1 Automata Let O be a (possibly infinite) set of output symbols. An automaton with outputs in O is a pair S = (S, #) consisting of a set S of states and a transition function # : S # O+ S. The transition function # specifies for a state s in S either an output o in O or a next state s # in S. The intuition is that in the first case, the computation is terminating, with observable output o; in the second case, the computation takes one step and...
for While Programs
, 1998
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of