27 research outputs found
Cut-off Theorems for the PV-model
We prove cut-off results for deadlocks and serializability of a -thread
run in parallel with itself: For a thread which accesses a set
of resources, each with a maximal capacity
, the PV-program , where copies of
are run in parallel, is deadlock free for all if and only if is
deadlock free where . This is a sharp
bound: For all and finite there
is a thread using these resources such that has a deadlock, but
does not for . Moreover, we prove a more general theorem: There are no
deadlocks in if and only if there are no deadlocks in
for any subset . For , is serializable for all if and only
if is serializable. For general capacities, we define a local obstruction
to serializability. There is no local obstruction to serializability in
for all if and only if there is no local obstruction to serializability in
for . The obstructions may be
found using a deadlock algorithm in . These serializability results
also have a generalization: If there are no local obstructions to
serializability in any of the -dimensional sub programs,
, then is serializable
04351 Abstracts Collection -- Spatial Representation: Discrete vs. Continuous Computational Models
From 22.08.04 to 27.08.04, the Dagstuhl Seminar 04351
``Spatial Representation: Discrete vs. Continuous Computational Models\u27\u27
was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Weak equivalence of higher-dimensional automata
This paper introduces a notion of equivalence for higher-dimensional
automata, called weak equivalence. Weak equivalence focuses mainly on a
traditional trace language and a new homology language, which captures the
overall independence structure of an HDA. It is shown that weak equivalence is
compatible with both the tensor product and the coproduct of HDAs and that,
under certain conditions, HDAs may be reduced to weakly equivalent smaller ones
by merging and collapsing cubes
A model category for the homotopy theory of concurrency
We construct a cofibrantly generated model structure on the category of flows
such that any flow is fibrant and such that two cofibrant flows are homotopy
equivalent for this model structure if and only if they are S-homotopy
equivalent. This result provides an interpretation of the notion of S-homotopy
equivalence in the framework of model categories.Comment: 45 pages ; 4 figure ; First paper corresponding to the content of
math.AT/0201252 ; final versio
Deadlock detection and dihomotopic reduction via progress shell decomposition
Deadlock detection for concurrent programs has traditionally been accomplished by symbolic methods or by search of a state transition system. This work examines an approach that uses geometric semantics involving the topological notion of dihomotopy to partition the state space into components, followed by an exhaustive search of the reduced state space. Prior work partitioned the state-space inductively; however, this work shows that a technique motivated by recursion further reduces the size of the state transition system. The reduced state space results in asymptotic improvements in overall runtime for verification. Thus, with efficient partitioning, more efficient deadlock detection and eventually more efficient verification of some temporal properties can be expected for large problems --Abstract, page iii
Weak equivalence of higher-dimensional automata
This paper introduces a notion of equivalence for higher-dimensional
automata, called weak equivalence. Weak equivalence focuses mainly on a
traditional trace language and a new homology language, which captures the
overall independence structure of an HDA. It is shown that weak equivalence is
compatible with both the tensor product and the coproduct of HDAs and that,
under certain conditions, HDAs may be reduced to weakly equivalent smaller ones
by merging and collapsing cubes.This research was partially supported by FCT (Fundacao para a Ciencia e a Tecnologia, Portugal) through project UID/MAT/00013/2013