1,471 research outputs found
Communicating Processes with Data for Supervisory Coordination
We employ supervisory controllers to safely coordinate high-level
discrete(-event) behavior of distributed components of complex systems.
Supervisory controllers observe discrete-event system behavior, make a decision
on allowed activities, and communicate the control signals to the involved
parties. Models of the supervisory controllers can be automatically synthesized
based on formal models of the system components and a formalization of the safe
coordination (control) requirements. Based on the obtained models, code
generation can be used to implement the supervisory controllers in software, on
a PLC, or an embedded (micro)processor. In this article, we develop a process
theory with data that supports a model-based systems engineering framework for
supervisory coordination. We employ communication to distinguish between the
different flows of information, i.e., observation and supervision, whereas we
employ data to specify the coordination requirements more compactly, and to
increase the expressivity of the framework. To illustrate the framework, we
remodel an industrial case study involving coordination of maintenance
procedures of a printing process of a high-tech Oce printer.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432
Money and Goldstone modes
Why is ``worthless'' fiat money generally accepted as payment for goods and
services? In equilibrium theory, the value of money is generally not
determined: the number of equations is one less than the number of unknowns, so
only relative prices are determined. In the language of mathematics, the
equations are ``homogeneous of order one''. Using the language of physics, this
represents a continuous ``Goldstone'' symmetry. However, the continuous
symmetry is often broken by the dynamics of the system, thus fixing the value
of the otherwise undetermined variable. In economics, the value of money is a
strategic variable which each agent must determine at each transaction by
estimating the effect of future interactions with other agents. This idea is
illustrated by a simple network model of monopolistic vendors and buyers, with
bounded rationality. We submit that dynamical, spontaneous symmetry breaking is
the fundamental principle for fixing the value of money. Perhaps the continuous
symmetry representing the lack of restoring force is also the fundamental
reason for large fluctuations in stock markets.Comment: 7 pages, 3 figure
Reactive Turing Machines
We propose reactive Turing machines (RTMs), extending classical Turing
machines with a process-theoretical notion of interaction, and use it to define
a notion of executable transition system. We show that every computable
transition system with a bounded branching degree is simulated modulo
divergence-preserving branching bisimilarity by an RTM, and that every
effective transition system is simulated modulo the variant of branching
bisimilarity that does not require divergence preservation. We conclude from
these results that the parallel composition of (communicating) RTMs can be
simulated by a single RTM. We prove that there exist universal RTMs modulo
branching bisimilarity, but these essentially employ divergence to be able to
simulate an RTM of arbitrary branching degree. We also prove that modulo
divergence-preserving branching bisimilarity there are RTMs that are universal
up to their own branching degree. Finally, we establish a correspondence
between executability and finite definability in a simple process calculus
Parallel Pushdown Automata and Commutative Context-Free Grammars in Bisimulation Semantics (Extended Abstract)
A classical theorem states that the set of languages given by a pushdown
automaton coincides with the set of languages given by a context-free grammar.
In previous work, we proved the pendant of this theorem in a setting with
interaction: the set of processes given by a pushdown automaton coincides with
the set of processes given by a finite guarded recursive specification over a
process algebra with actions, choice, sequencing and guarded recursion, if and
only if we add sequential value passing. In this paper, we look what happens if
we consider parallel pushdown automata instead of pushdown automata, and a
process algebra with parallelism instead of sequencing.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.05788. arXiv admin note:
text overlap with arXiv:2203.0171
Expressiveness modulo Bisimilarity of Regular Expressions with Parallel Composition (Extended Abstract)
The languages accepted by finite automata are precisely the languages denoted
by regular expressions. In contrast, finite automata may exhibit behaviours
that cannot be described by regular expressions up to bisimilarity. In this
paper, we consider extensions of the theory of regular expressions with various
forms of parallel composition and study the effect on expressiveness. First we
prove that adding pure interleaving to the theory of regular expressions
strictly increases its expressiveness up to bisimilarity. Then, we prove that
replacing the operation for pure interleaving by ACP-style parallel composition
gives a further increase in expressiveness. Finally, we prove that the theory
of regular expressions with ACP-style parallel composition and encapsulation is
expressive enough to express all finite automata up to bisimilarity. Our
results extend the expressiveness results obtained by Bergstra, Bethke and
Ponse for process algebras with (the binary variant of) Kleene's star
operation.Comment: In Proceedings EXPRESS'10, arXiv:1011.601
Pushdown Automata and Context-Free Grammars in Bisimulation Semantics
The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings. In the Reactive Turing Machine, transitions have labels to give a notion of interactivity. In the resulting process graph, we use bisimilarity instead of language equivalence.
Subsequently, we considered other classical theorems and notions from automata theory and formal languages theory. In this paper, we consider the classical theorem of the correspondence between pushdown automata and context-free grammars. By changing the process operator of sequential composition to a sequencing operator with intermediate acceptance, we get a better correspondence in our setting. We find that the missing ingredient to recover the full correspondence is the addition of a notion of state awareness
A Process Algebra for Supervisory Coordination
A supervisory controller controls and coordinates the behavior of different
components of a complex machine by observing their discrete behaviour.
Supervisory control theory studies automated synthesis of controller models,
known as supervisors, based on formal models of the machine components and a
formalization of the requirements. Subsequently, code generation can be used to
implement this supervisor in software, on a PLC, or embedded microprocessor. In
this article, we take a closer look at the control loop that couples the
supervisory controller and the machine. We model both event-based and
state-based observations using process algebra and bisimulation-based
semantics. The main application area of supervisory control that we consider is
coordination, referred to as supervisory coordination, and we give an academic
and an industrial example, discussing the process-theoretic concepts employed.Comment: In Proceedings PACO 2011, arXiv:1108.145
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