Actors without Directors: A Kahnian View of Heterogeneous Systems

Caspi, Paul; Benveniste, Albert; Lublinerman, Roberto; Tripakis, Stavros

doi:10.1007/978-3-642-00602-9_4

Cited by 13 publications

(11 citation statements)

References 14 publications

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“…. Thus, in our framework, signals may not assume meaningful values (2 D) at certain tags followed by meaningful values at some subsequent tags similar to the convention followed in [23]. For example, in a behavior , let the spd submodule of the module T r be specified to assign acceleration values (tr:a) from a certain instant as 0:5 km=s 2 after 1 min, 0:4 km=s 2 after 3 min, 0:2 km=s 2 after 4 min, and 0:3 km=s 2 after 5 min.…”

Section: The Order Structure Of Tagged Signals In a Tsmmentioning

confidence: 98%

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A Kleene Algebra of Tagged System Actors for Reasoning about Heterogeneous Embedded Systems

Dey

Sarkar

Basu

2013

IEEE Trans. Comput.

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The tagged signal model (TSM) is a formal framework for modeling heterogeneous embedded systems. In the present work, we provide a representation of tagged systems using the semantics of Kleene algebra. We further illustrate mechanisms for both behavioral transformational verification through equivalence checking and property verification of heterogeneous embedded systems based on this algebraic representation.

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Section: The Order Structure Of Tagged Signals In a Tsmmentioning

confidence: 98%

“…When AE is clear from the context, we shall denote this set simply as S v . Following [23], we now define a prefix ordering v on the set S v of signals. For any two signals s 1 ; s 2 2 S v , s 1 v s 2 (read as s 1 is contained in s 2 ) iff 8 2 T ½s 1 ðÞ 6 ¼ s 2 ðÞ ) 8 0 !…”

Section: The Order Structure Of Tagged Signals In a Tsmmentioning

confidence: 99%

A Kleene Algebra of Tagged System Actors for Reasoning about Heterogeneous Embedded Systems

Dey

Sarkar

Basu

2013

IEEE Trans. Comput.

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“…9 A generalized ultrametric space A, P, , 0, d is Cauchy-complete if and only if for every sequence an | n ∈ ω over A, if an | n ∈ ω is Cauchy 10 in A, P, , 0, d , then there is a ∈ A such that for every p ∈ P such that p = 0, there is n ∈ ω such that for every n > n, d(a n , a) < p. 11 10 For every generalized ultrametric space A, P, , 0, d , a sequence an | n ∈ ω over A is Cauchy in A, P, , 0, d if and only if for every p ∈ P such that p = 0, there is n ∈ ω such that for every n 1 , n 2 > n, d(an 1 , an 2 ) < p. 11 We write ω for the least limit ordinal. 12 For every function f and every set A, we write f A for the restriction of f to A, namely the function { a, b | a, b ∈ f and a ∈ A}.…”

Section: The Generalized Distance Functionmentioning

confidence: 99%

On Fixed Points of Strictly Causal Functions

Matsikoudis

Lee

2013

Lecture Notes in Computer Science

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We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on tagged signals, and argue that these strictly contracting functions are actually the functions that one ought to be interested in. We prove a constructive fixed-point theorem for these functions, introduce a corresponding induction principle, and study the related convergence process.

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“…in contradiction to (9). 19 An ordered set P, is a semilattice if and only if every non-empty finite subset of P has a greatest lower bound in P, .…”

mentioning

confidence: 99%

On Fixed Points of Strictly Causal Functions

Matsikoudis¹,

Lee²

2013

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. We ask whether strictly causal components form well de ned systems when arranged in feedback con gurations. The standard interpretation for such con gurations induces a xed-point constraint on the function modelling the component involved. We de ne strictly causal functions formally, and show that the corresponding xed-point problem does not always have a well de ned solution. We examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on tagged signals, and argue that these strictly contracting functions are actually the functions that one ought to be interested in. We prove a constructive xed-point theorem for these functions, introduce a corresponding induction principle, and study the related convergence process. All rights reserved.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. AcknowledgementThis work was supported in part by the Center for Hybrid and Embedded Software Systems (CHESS) at UC Berkeley, which receives support from the National Science Foundation (NSF awards #0720882 (CSR-EHS: PRET), #0931843 (CPS: Large: ActionWebs), and #1035672 (CPS: Medium: Ptides)), the Naval Research Laboratory (NRL #N0013-12-1-G015), and the following companies: Bosch, National Instruments, and Toyota.On Fixed Points of Strictly Causal Functions * Eleftherios Matsikoudis Edward A. Lee AbstractWe ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We examine the relationship between these functions and the functions that are strictly contracting with re...

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Actors without Directors: A Kahnian View of Heterogeneous Systems

Cited by 13 publications

References 14 publications

A Kleene Algebra of Tagged System Actors for Reasoning about Heterogeneous Embedded Systems

A Kleene Algebra of Tagged System Actors for Reasoning about Heterogeneous Embedded Systems

On Fixed Points of Strictly Causal Functions

On Fixed Points of Strictly Causal Functions

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