Results 11  20
of
28
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
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...
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 ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
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
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. Subsequently we ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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...
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
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.
General System Identification—Fundamentals and Results I.
"... The term identification was introduced by Zadeh (1956) as a generic expression for the problem ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
The term identification was introduced by Zadeh (1956) as a generic expression for the problem
1977b), “Progress in General Systems Research
 Proceedings of First International Conference on Applied General Systems Research: Recent Developments and Trends
"... ..."
Bisimulations and Behaviour of Nondeterministic Automata
, 1999
"... The minimization of nondeterministic automata without initial states (developed within a gametheoretic framework in Calude, Calude, Khoussainov [3]) is presented in terms of bisimulations; the minimal automaton is unique up to an isomorphism in case of reversible automata. We also prove that there ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The minimization of nondeterministic automata without initial states (developed within a gametheoretic framework in Calude, Calude, Khoussainov [3]) is presented in terms of bisimulations; the minimal automaton is unique up to an isomorphism in case of reversible automata. We also prove that there exists an infinite class of (strongly connected) nondeterministic automata each of which is not bisimilar with any deterministic automaton. This shows that in the sense of bisimilarity nondeterministic automata are more powerful than deterministic ones. It is an open question whether the method of bisimulations can produced, in general, the unique minimal nondeterministic automaton.
Realization of Probabilistic Automata: Categorical Approach
 Recent Developments in Algebraic Development Techniques  Selected Papers, volume 1827 of Lecture Notes in Computer Science. SpringerVerlag. In print
"... . We present a categorical framework to study probabilistic automata starting by obtaining aggregation and interconnection as universal constructions. We also introduce the notion of probabilistic behavior in order to get adjunctions between probabilistic behavior and probabilistic automata. Thus we ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. We present a categorical framework to study probabilistic automata starting by obtaining aggregation and interconnection as universal constructions. We also introduce the notion of probabilistic behavior in order to get adjunctions between probabilistic behavior and probabilistic automata. Thus we are able to extend to the probabilistic setting free and minimal realizations as universal constructions. 1 Introduction Probabilistic automata [Rab63,Paz66] are central in the theory of unreliable systems, namely for providing the appropriate semantic domain (see for instance [BDEP97,LS91,vGSST95]). In particular we adopt the Moore model, that is, the outputs are assigned to the states. In [MSS99,SM99] we provided a (pre)categorical characterization for several combinations of probabilistic automata. However, we had to work with structures weaker than categories [Ehr65,Cop80] because composition of morphisms was not always dened. Herein we adopt a dierent approach by considering that th...