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Tossing Algebraic Flowers down the Great Divide
 In People and Ideas in Theoretical Computer Science
, 1999
"... Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly l ..."
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Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly languages that allowed symbolic codes for operations and addresses. fortran began the spread of "high level" programming languages, though at the time it was strongly opposed by many assembly programmers; important features that developed later include blocks, recursive procedures, flexible types, classes, inheritance, modules, and genericity. Without going into the philosophical problems raised by abstraction (which in view of the discussion of realism in Section 4 may be considerable), it seems clear that the mathematics used to describe programming concepts should in general get more abstract as the programming concepts get more abstract. Nevertheless, there has been great resistance to u...
ObjectOriented Hybrid Systems of Coalgebras plus Monoid Actions
 Algebraic Methodology and Software Technology (AMAST
, 1996
"... . Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (nontempora ..."
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. Hybrid systems combine discrete and continuous dynamics. We introduce a semantics for such systems consisting of a coalgebra together with a monoid action. The coalgebra captures the (discrete) operations on a state space that can be used by a client (like in the semantics of ordinary (nontemporal) objectoriented systems). The monoid action captures the influence of time on the state space, where the monoids that we consider are the natural numbers monoid (N; 0; +) of discrete time, and the positive reals monoid (R0 ; 0; +) of real time. Based on this semantics we develop a hybrid specification formalism with timed method applications: it involves expressions like s:meth@ff, with the following meaning: in state s let the state evolve for ff units of time (according to the monoid action), and then apply the (coalgebraic) method meth. In this formalism we specify various (elementary) hybrid systems, investigate their correctness, and display their behaviour in simulations. We furthe...
Symbolic models for control systems
, 2007
"... In this paper we provide a bridge between the infinite state models used in control theory to describe the evolution of continuous physical processes and the finite state models used in computer science to describe software. We identify classes of control systems for which it is possible to constru ..."
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In this paper we provide a bridge between the infinite state models used in control theory to describe the evolution of continuous physical processes and the finite state models used in computer science to describe software. We identify classes of control systems for which it is possible to construct equivalent (bisimilar) finite state models. These constructions are based on finite, but otherwise arbitrary, partitions of the set of inputs or outputs of a control system.
Approximate identification of automata
 Electronics Letters
, 1975
"... A technique is described for the identification of probabilistic and other nondeterministic automata from sequences of their input/output behaviour. For a given number of states the models obtained are optimal in well defined senses, one related to leastmeansquare approximation and the other to S ..."
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A technique is described for the identification of probabilistic and other nondeterministic automata from sequences of their input/output behaviour. For a given number of states the models obtained are optimal in well defined senses, one related to leastmeansquare approximation and the other to Shannon entropy. Practical and theoretical investigations of the technique are outlined. 1
Automata and Behaviours in Categories of Processes
, 1996
"... An early result of Goguen [4, 5] describes the fundamental adjunction between categories of deterministic automata and their behaviours. Our first step is to redefine (morphisms in) these categories of automata and behaviours so that a restriction in Goguen's approach can be avoided. Subsequent ..."
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An early result of Goguen [4, 5] describes the fundamental adjunction between categories of deterministic automata and their behaviours. Our first step is to redefine (morphisms in) these categories of automata and behaviours so that a restriction in Goguen's approach can be avoided. Subsequently we give a coalgebraic analysis of this behaviourrealization adjunction; it yields a second generalization to other types of (not only deterministic) automata (and their behaviours). We further show that our (redefined) categories of automata and behaviours support elementary process combinators like renaming, restriction, parallel composition, replication and feedback (some of which also occur, for example, in the calculus). One of the main contributions is that replication !P is defined for an automaton P such that !P is the terminal coalgebra !P = ! Pk!P of the functor Pk(\Gamma) "compose with P ". The behaviour functor from automata to their behaviours preserves these process combinato...
A bialgebraic review of regular expressions, deterministic automata and languages
 Techn. Rep. ICISR05003, Inst. for Computing and Information Sciences, Radboud Univ
, 2005
"... To Joseph Goguen on the occasion of his 65th birthday1. Abstract. This papers reviews the classical theory of deterministic automata and regular languages from a categorical perspective. The basis is formed by Rutten’s description of the Brzozowski automaton structure in a coalgebraic framework. We ..."
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To Joseph Goguen on the occasion of his 65th birthday1. Abstract. This papers reviews the classical theory of deterministic automata and regular languages from a categorical perspective. The basis is formed by Rutten’s description of the Brzozowski automaton structure in a coalgebraic framework. We enlarge the framework to a socalled bialgebraic one, by including algebras together with suitable distributive laws connecting the algebraic and coalgebraic structure of regular expressions and languages. This culminates in a reformulated proof via finality of Kozen’s completeness result. It yields a complete axiomatisation of observational equivalence (bisimilarity) on regular expressions. We suggest that this situation is paradigmatic for (theoretical) computer science as the study of “generated behaviour”.
INTERCONNECTION OF PROBABILISTIC SYSTEMS
, 2000
"... There is a growing interest in models for probabilistic systems. This fact is motivated by engineering applications, namely in problems concerning the evaluation of the performance of systems. It is of ..."
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There is a growing interest in models for probabilistic systems. This fact is motivated by engineering applications, namely in problems concerning the evaluation of the performance of systems. It is of
An Exact Algebraic Characterization Of Behavioral Subtyping
 PREPRINT N'UM. 315, CENTRE DE RECERCA MATEM'ATICA, ISTITUT D'ESTUDIS CATALANS (DESEMBRE
, 1995
"... A model theory for correct behavioral subtyping for abstract data types (with immutable objects) is developed within the framework of the behaviorrealization adjunction. To allow for incomplete specifications, proofs of correct behavioral subtyping are based on comparison to one of several parad ..."
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A model theory for correct behavioral subtyping for abstract data types (with immutable objects) is developed within the framework of the behaviorrealization adjunction. To allow for incomplete specifications, proofs of correct behavioral subtyping are based on comparison to one of several paradigmatic models. For specifications that are not termgenerated, these results are the first complete algebraic characterizations of behavioral subtyping.
The role of randomness in cybernetic systems
 PROCEEDINGS OF CYBERNETICS SOCIETY CONFERENCE ON RECENT TOPICS IN CYBERNETICS, LONDON 20TH SEPTEMBER 1974
, 1974
"... This paper demonstrates that random phenomena, although most often treated in the context of system malfunction, can play major constructive roles in the philosophy, theory and application of cybernetic systems. A controltheoretic example is given to show that a simple stochastic automaton can solv ..."
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This paper demonstrates that random phenomena, although most often treated in the context of system malfunction, can play major constructive roles in the philosophy, theory and application of cybernetic systems. A controltheoretic example is given to show that a simple stochastic automaton can solve a regulator problem otherwise requiring a recursive automaton, and insoluble for finitestate automata. An identificationtheoretic example is given to show that the assumption of causality in modelling a simple acausal system can lead to models which grow in size, on average, precisely at the rate of acquisition of observations. The significance and applications of these results are discussed and illustrated. Finally, it is suggested that the interpretation of stochastic automata theory in terms of system malfunction is far too restrictive in its stimulation of theoretical developments. A wider view of the role of random phenomena might aid the development of results and techniques which actually deliver what automata theory has always seemed to promise.