1,141 research outputs found
Equivalence-Checking on Infinite-State Systems: Techniques and Results
The paper presents a selection of recently developed and/or used techniques
for equivalence-checking on infinite-state systems, and an up-to-date overview
of existing results (as of September 2004)
Beyond Language Equivalence on Visibly Pushdown Automata
We study (bi)simulation-like preorder/equivalence checking on the class of
visibly pushdown automata and its natural subclasses visibly BPA (Basic Process
Algebra) and visibly one-counter automata. We describe generic methods for
proving complexity upper and lower bounds for a number of studied preorders and
equivalences like simulation, completed simulation, ready simulation, 2-nested
simulation preorders/equivalences and bisimulation equivalence. Our main
results are that all the mentioned equivalences and preorders are
EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly
one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for
visibly one-counter automata improves also the previously known DP-hardness
results for ordinary one-counter automata and one-counter nets. Finally, we
study regularity checking problems for visibly pushdown automata and show that
they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC
Equivalence of infinite-state systems with silent steps
This dissertation contributes to analysis methods for infinite-state systems. The dissertation focuses on equivalence testing for two relevant classes of infinite-state systems: commutative context-free processes, and one-counter automata. As for equivalence notions, we investigate the classical bisimulation and simulation equivalences. The important point is that we allow for silent steps in the model, abstracting away from internal, unobservable actions. Very few decidability results have been known so far for bisimulation or simulation equivalence for infinite-state systems with silent steps, as presence of silent steps makes the equivalence problem arguably harder to solve. A standard technique for bisimulation or simulation equivalence testing is to use the hierarchy of approximants. For an effective decision procedure the hierarchy must stabilize (converge) at level omega, the first limit ordinal, which is not the case for the models investigated in this thesis. However, according to a long-standing conjecture, the community believed that the convergence actually takes place at level omega+ omega in the class of commutative context free processes. We disprove the conjecture and provide a lower bound of omega * omega for the convergence level. We also show that all previously known positive decidability results for BPPs can be re-proven uniformly using the improved approximants techniques. Moreover dissertation contains an unsuccesfull attack on one of the main open problems in the area: decidability of weak bisimulation equivalence for commutative context-free processes. Our technical development of this section is not sufficient to solve the problem, but we believe it is a serious step towards a solution. Furtermore, we are able to show decidability of branching (stuttering) bisimulation equivalence, a slightly more discriminating variant of bisimulation equivalence. It is worth emphesizing that, until today, our result is the only known decidability result for bisimulation equivalence in a class of inifinite-state systems with silent steps that is not known to admit convergence of (some variant of) standard approximants at level omega. Finally we consider weak simulation equivalence over one-counter automata without zero tests (allowing zero tests implies undecidability). While weak bisimulation equivalence is known to be undecidable in this class, we prove a surprising result that weak simulation equivalence is actually decidable. Thus we provide a first example going against a trend, widely-believed by the community, that simulation equivalence tends to be computationally harder than bisimulation equivalence. In short words, the dissertation contains three new results, each of them solving a non-trivial open problem about equivalence testing of infinite-state systems with silent steps
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
Sequential Composition in the Presence of Intermediate Termination (Extended Abstract)
The standard operational semantics of the sequential composition operator
gives rise to unbounded branching and forgetfulness when transparent process
expressions are put in sequence. Due to transparency, the correspondence
between context-free and pushdown processes fails modulo bisimilarity, and it
is not clear how to specify an always terminating half counter. We propose a
revised operational semantics for the sequential composition operator in the
context of intermediate termination. With the revised operational semantics, we
eliminate transparency, allowing us to establish a close correspondence between
context-free processes and pushdown processes. Moreover, we prove the reactive
Turing powerfulness of TCP with iteration and nesting with the revised
operational semantics for sequential composition.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.00049. arXiv admin note:
substantial text overlap with arXiv:1706.0840
Decidable Models of Recursive Asynchronous Concurrency
Asynchronously communicating pushdown systems (ACPS) that satisfy the
empty-stack constraint (a pushdown process may receive only when its stack is
empty) are a popular decidable model for recursive programs with asynchronous
atomic procedure calls. We study a relaxation of the empty-stack constraint for
ACPS that permits concurrency and communication actions at any stack height,
called the shaped stack constraint, thus enabling a larger class of concurrent
programs to be modelled. We establish a close connection between ACPS with
shaped stacks and a novel extension of Petri nets: Nets with Nested Coloured
Tokens (NNCTs). Tokens in NNCTs are of two types: simple and complex. Complex
tokens carry an arbitrary number of coloured tokens. The rules of NNCT can
synchronise complex and simple tokens, inject coloured tokens into a complex
token, and eject all tokens of a specified set of colours to predefined places.
We show that the coverability problem for NNCTs is Tower-complete. To our
knowledge, NNCT is the first extension of Petri nets, in the class of nets with
an infinite set of token types, that has primitive recursive coverability. This
result implies Tower-completeness of coverability for ACPS with shaped stacks
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