2,131 research outputs found
Wadge Degrees of -Languages of Petri Nets
We prove that -languages of (non-deterministic) Petri nets and
-languages of (non-deterministic) Turing machines have the same
topological complexity: the Borel and Wadge hierarchies of the class of
-languages of (non-deterministic) Petri nets are equal to the Borel and
Wadge hierarchies of the class of -languages of (non-deterministic)
Turing machines which also form the class of effective analytic sets. In
particular, for each non-null recursive ordinal there exist some -complete and some -complete -languages of Petri nets, and the supremum of
the set of Borel ranks of -languages of Petri nets is the ordinal
, which is strictly greater than the first non-recursive ordinal
. We also prove that there are some -complete, hence non-Borel, -languages of Petri nets, and
that it is consistent with ZFC that there exist some -languages of
Petri nets which are neither Borel nor -complete. This
answers the question of the topological complexity of -languages of
(non-deterministic) Petri nets which was left open in [DFR14,FS14].Comment: arXiv admin note: text overlap with arXiv:0712.1359, arXiv:0804.326
Forward Analysis and Model Checking for Trace Bounded WSTS
We investigate a subclass of well-structured transition systems (WSTS), the
bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete
deterministic ones, which we claim provide an adequate basis for the study of
forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth.
Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered
previously for the termination of forward analysis, boundedness is decidable.
Boundedness turns out to be a valuable restriction for WSTS verification, as we
show that it further allows to decide all -regular properties on the
set of infinite traces of the system
Complexity of Problems of Commutative Grammars
We consider commutative regular and context-free grammars, or, in other
words, Parikh images of regular and context-free languages. By using linear
algebra and a branching analog of the classic Euler theorem, we show that,
under an assumption that the terminal alphabet is fixed, the membership problem
for regular grammars (given v in binary and a regular commutative grammar G,
does G generate v?) is P, and that the equivalence problem for context free
grammars (do G_1 and G_2 generate the same language?) is in
On the Decidability of Non Interference over Unbounded Petri Nets
Non-interference, in transitive or intransitive form, is defined here over
unbounded (Place/Transition) Petri nets. The definitions are adaptations of
similar, well-accepted definitions introduced earlier in the framework of
labelled transition systems. The interpretation of intransitive
non-interference which we propose for Petri nets is as follows. A Petri net
represents the composition of a controlled and a controller systems, possibly
sharing places and transitions. Low transitions represent local actions of the
controlled system, high transitions represent local decisions of the
controller, and downgrading transitions represent synchronized actions of both
components. Intransitive non-interference means the impossibility for the
controlled system to follow any local strategy that would force or dodge
synchronized actions depending upon the decisions taken by the controller after
the last synchronized action. The fact that both language equivalence and
bisimulation equivalence are undecidable for unbounded labelled Petri nets
might be seen as an indication that non-interference properties based on these
equivalences cannot be decided. We prove the opposite, providing results of
decidability of non-interference over a representative class of infinite state
systems.Comment: In Proceedings SecCo 2010, arXiv:1102.516
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)
Scale-invariant cellular automata and self-similar Petri nets
Two novel computing models based on an infinite tessellation of space-time
are introduced. They consist of recursively coupled primitive building blocks.
The first model is a scale-invariant generalization of cellular automata,
whereas the second one utilizes self-similar Petri nets. Both models are
capable of hypercomputations and can, for instance, "solve" the halting problem
for Turing machines. These two models are closely related, as they exhibit a
step-by-step equivalence for finite computations. On the other hand, they
differ greatly for computations that involve an infinite number of building
blocks: the first one shows indeterministic behavior whereas the second one
halts. Both models are capable of challenging our understanding of
computability, causality, and space-time.Comment: 35 pages, 5 figure
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Computer-aided analysis of concurrent systems
The introduction of concurrency into programs has added to the complexity of the software design process. This is most evident in the design of communications protocols where concurrency is inherent to the behavior of the system. The complexity exhibited by such software systems makes more evident the needs for computer-aided tools for automatically analyzing behavior.The Distributed Systems project at UCI has been developing a suite of tools, based on Petri nets, which support the design and evaluation of concurrent software systems. This paper focuses attention on one of the tools: the reachability graph analyzer (RGA). This tool provides mechanisms for proving general system properties (e.g., deadlock-freeness) as well as system-specific properties. The tool is sufficiently general to allow a user to apply complex user-defined analysis algorithms to reachability graphs. The alternating-bit protocol with a bounded channel is used to demonstrate the power of the tool and to point to future extensions
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