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12
Observational logic
 IN ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY (AMAST'98
, 1999
"... We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required ..."
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Cited by 56 (10 self)
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We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required to be compatible with the indistinguishability relation determined by the given observers. In particular, we introduce a homomorphism concept for observational algebras which adequately expresses observational relationships between algebras. Then we consider a flexible notion of observational signature morphism which guarantees the satisfaction condition of institutions w.r.t. observational satisfaction of arbitrary firstorder sentences. From the proof theoretical point of view we construct a sound and complete proof system for the observational consequence relation. Then we consider structured observational specifications and we provide a sound and complete proof system for such specifications by using a general, institutionindependent result of [6].
On the integration of observability and reachability concepts
 Foundations of Software Science and Computation Structures, LNCS
, 2002
"... 2 Institut f"ur Informatik, LudwigMaximiliansUniversit"at M"unchen, Germany ..."
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Cited by 21 (2 self)
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2 Institut f&quot;ur Informatik, LudwigMaximiliansUniversit&quot;at M&quot;unchen, Germany
Observational Logic, ConstructorBased Logic, and their Duality
, 2002
"... Observability and reachability are important concepts for formal software development. While observability concepts are used to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this p ..."
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Cited by 13 (1 self)
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Observability and reachability are important concepts for formal software development. While observability concepts are used to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper we first reconsider the observational logic institution which provides a logical framework for dealing with observability. Then we develop in a completely analogous way the constructorbased logic institution which formalizes a novel treatment of reachability. Both institutions are tailored to capture the semantically correct realizations of a specification from either the observational or the reachability point of view. We show that there is a methodological and even formal duality between both frameworks. In particular, we establish a correspondence between observer operations and datatype constructors, observational and constructorbased algebras, fully abstract and reachable algebras, and observational and inductive consequences of specifications. The formal duality between the observability and reachability concepts is established in a categorytheoretic setting.
Brzozowski’s algorithm (co)algebraically
"... Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctn ..."
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Cited by 12 (4 self)
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Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. 1
A AlgebraCoalgebra Duality in Brzozowski’s Minimization Algorithm
"... We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simpl ..."
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Cited by 8 (3 self)
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We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. Notably, we derive algorithms to obtain minimal, language equivalent automata from Moore, nondeterministic and weighted automata.
Dialgebraic Specification and Modeling
"... corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube ..."
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Cited by 4 (4 self)
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corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube
On the Integration of Observability and . . .
 FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES, LNCS
, 2002
"... This paper focuses on the integration of reachability and observability concepts within an algebraic, institutionbased framework. We develop the essential notions that are needed to construct an institution which takes into account both the generation and observationoriented aspects of software ..."
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This paper focuses on the integration of reachability and observability concepts within an algebraic, institutionbased framework. We develop the essential notions that are needed to construct an institution which takes into account both the generation and observationoriented aspects of software systems. Thereby the underlying paradigm is that the semantics of a specification should be as loose as possible to capture all its correct realizations. We also consider the socalled "idealized models" of a specication which are useful to study the behavioral properties a user can observe when he/she is experimenting with the system. Finally, we present sound and complete proof systems that allow us to derive behavioral properties from the axioms of a given specification.
MFPS 2013 Varieties and covarieties of languages (preliminary version)
"... Because of the isomorphism (X × A) → X ∼ = X → (A → X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebracoalgebra duality goes back to Arbib and Manes, who formulated it as a ..."
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Because of the isomorphism (X × A) → X ∼ = X → (A → X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebracoalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalman’s duality in systems theory between controllability and observability. Recently, it was used to give a new proof of Brzozowski’s minimization algorithm for deterministic automata. Here we will use the algebracoalgebra duality of automata as a common perspective for the study of both varieties and covarieties, which are classes of automata and languages defined by equations and coequations, respectively. We make a first connection with Eilenberg’s definition of varieties of languages, which is based on the classical, algebraic notion of varieties of (transition) monoids. Keywords:
CNRS,ENSLyon,Université de Lyon LIP (UMR 5668)
"... Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctn ..."
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Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. This paper is dedicated to Dexter Kozen on the occasion of his 60th birthday. Dexter always seeks simplicity and crystalclear proofs in his research: “a beautiful result deserves a beautiful proof ” could be the motto of his work. This paper is a tribute to that ⋆. 1
Varieties and Covarieties of Languages
"... Because of the isomorphism (X × A) → X ∼ = X → (A → X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebracoalgebra duality goes back to Arbib and Manes, who formulated it as a ..."
Abstract
 Add to MetaCart
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Because of the isomorphism (X × A) → X ∼ = X → (A → X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebracoalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalman’s duality in systems theory between controllability and observability. Recently, it was used to give a new proof of Brzozowski’s minimization algorithm for deterministic automata. Here we will use the algebracoalgebra duality of automata as a common perspective for the study of both varieties and covarieties, which are classes of automata and languages defined by equations and coequations, respectively. We make a first connection with Eilenberg’s definition of varieties of languages, which is based on the classical, algebraic notion of varieties of (transition) monoids.