Showing papers on "Realizability published in 1990"

Distributed reactive systems are hard to synthesize

Abstract: The problem of synthesizing a finite-state distributed reactive system is considered. Given a distributed architecture A, which comprises several processors P/sub 1/, . . ., P/sub k/ and their interconnection scheme, and a propositional temporal specification phi , a solution to the synthesis problem consists of finite-state programs Pi /sub 1/, . . ., Pi /sub k/ (one for each processor), whose joint (synchronous) behavior maintains phi against all possible inputs from the environment. Such a solution is referred to as the realization of the specification phi over the architecture A. Specifically, it is shown that the problem of realizing a given propositional specification over a given architecture is undecidable, and it is nonelementarily decidable for the very restricted class of hierarchical architectures. An extensive characterization of architecture classes for which the realizability problem is elementarily decidable and of classes for which it is undecidable is given. >

Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity

Abstract: CONTENTS § 1. Introduction § 2. Realizability theorem § 3. Tagged skeletons § 4. Coding integrable Hamiltonian systems References

On a geometrical interpretation of differential-algebraic equations

Abstract: The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE, and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lower-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena.

Einstein's equations and realizability of CR manifolds

Abstract: It is shown that the vacuum Einstein equations imposed on a metric which admits shear-free null and geodesic congruence imply the realizability of an associated CR structure.

Effective domains and intrinsic structure

Abstract: Topos theory is the categorical analog of constructive set theory; and conveniently, PERs (partial equivalence relations) do sit inside a topos-the category of PERs can be (loosely speaking) identified with the full subcategory of modest sets in Hyland's effective topos. (The effective topos is the topos-theoretic version of recursive realizability.) Working in the effective topos is especially attractive since not only can set-theoretic reasoning be used, but one also has a lot of category-theoretic and topos-theoretic machinery at one's disposal. That is the point of view taken in this research. The basic theory of Sigma -spaces is discussed. A convex power domain is also presented. Modal operators are outlined. Parallelism and sheaves are examined. Finally, the fixed-point classifier is presented. >

Advances in asynchronous circuit theory. Part I : gate and unbounded inertial delay

Abstract: Although the theory of asynchronous circuits (fates back to the early 1950s, considerable progress has been made in this area in the past five years This paper constitutes the first part of a two-part survey of the recent advances in this field Part I of the survey presents a unified and concise overview of those aspects of the theory that (leaf with the behavior of circuits under the assumption that delays in the circuit components and wires are unbounded The historical development of the subject is presented, and some shortcomings of the earlier approaches are discussed Ternary simulation is related to the binary analysis methods; the ternary approach is then used to correct the flaws in the earlier work The question of realizability of sequential behaviors is then considered It is shown that the class of realizable behaviors is rather severely restricted by the unbounded-delay assumption and that the use of bounded-delay models is more realistic Part 11 of the survey will deal with bounded-delay models, MOS circuits, classical and delay-insensitive design methods, and complexity issues

An algorithm for tree-realizability of distance matrices ∗

Abstract: An algorithm for testing tree realizability of distance matrices is given. It is well-known that if a matrix D has a realization by a tree then such a realization is optimal and unique up to homeomorphism. Our algorithm produces a tree realization or a message that there is no such realization in time O(n 2) where n is the number of points in a finite metric space with the distance matrix D. An O(n 2) algorithm for computing distance matrix for a given tree is also given.

Input/Output Equations and Realizability

Abstract: This paper establishes a precise correspondence between realizability and the existence of algebraic differential equations relating derivatives of inputs and outputs of a continuous time system. The only assumption needed is that the data be “well-posed” in a suitable sense. Our results serve to relate the notion of realizability proposed by Fliess in the context of differential algebra with the more standard concept used in nonlinear state-space systems.

A 'neural' A/D converter utilizing Schmitt trigger

Abstract: Theoretical considerations are presented regarding the stability and the physical realizability of a new A/D converter based on the Hopfield neural network. The equivalent circuit made and described by M.J.S. Smith and C.L. Portmann (1989) is analyzed in order to solve the problem in a different way. The authors adopt the same circuit scheme realized with Schmitt triggers, but modifying their hysteresis and thresholds in an appropriate manner. The role played by the amplifier response time is widely illustrated, and the network theoretical behavior is analyzed. A proof that validates the correct operation of the circuits is reported. >

Relating Kripke models and realizability

Abstract: The principal undertaking of this thesis is to investigate, as constructively as possible some of the connections between two fundamental paradigms of intuitionistic semantics: Kripke-Beth models, and generalizations thereof, and realizability interpretations. The former captures truth-value semantics for constructive reasoning, the latter semantics based on evidence: codes, proofs, or recursive indices that attest to the truth of logical statements. Connections between these two ideas have been investigated by Hyland in the realizability to Kripke model direction, and by Lauchli in the other direction. Here we explore alternatives to the former, and more constructive versions of the latter. In chapter one we construct a Kripke model for syntactic realizability for Heyting Arithmetc. In the second chapter we describe an abstract realizability interpretation (along the lines of Beeson, Feferman, Troelstra-van Dalen) and construct an elementarily equivalent Kripke model. In chapter three, using a translation of the intuitionistic completeless theorem for Beth semantics due to Veldman, de Swart, van Dalen and others, we build a family of completely constructive Beth models for a general family of realizabilities. In chapter four, a partial converse to these results is established. We show that to every countable Kripke model there corresponds an elementarily equivalent realizability notion, in which the realizers are a collection of functions which include the partial recursive functions, but are no more complex than the partial recursive functions relativized to the diagram of the Kripke model as an oracle.

A note on guarded recursion

Abstract: We introduce a logical notion of well-guardedness for recursive terms on arbitrary signatures defined in Plotkin's framework of structural operational specifications, restricted by de Simone's realizability requirements. We then suggest a simpler form for the logical rule that gives the behaviour of a recursively defined expression in terms of the behaviour of its unfoldings. For well-guarded terms, the simplified rule is logically equivalent to the general rule, but is has not the draw-back to ask for premises more complex that consequences.

Safe Positive Induction in the Programming Logic TK

Abstract: We describe an alternative schema of induction for the programming logic TK based on safe positive induction. This replaces the original schema based on the well founded part of a relation. We show how the new schema can be included into the realizability definition and how the soundness of realizability can be extended to allow for the derivation of recursive programs from proofs of specifications which use the new schema. We further show how systems of mutual induction can be handled naturally with the new schema. In particular we show how useful systems of mutually recursive combinators can be derived which realize the principles of mutual induction.

The realization problem for a class of nonlinear systems

Abstract: This paper studies the realization problem for a class of nonlinear systems. Necessary and sufficient conditions are contained for realizability of a system and an algorithm is presented for the construction of a realization.

Realisierbarkeit von darstellungen endlicher gruppen in einheitswurzelkörpern

Abstract: LetD:G→GL(n,C) be an irreducible linear representation of a finite groupG with the characterX. IfD is realizible in Q(ξm) and Q(ξm′) we give a condition for then realizability ofD in Q(ξ(m′)). If the degreen is a prime ≠ 2, we show thatD realizible in Q(ξf), wheref is the conductor of the abelian extensionQ(X)/Q.