292,235 research outputs found
Unique Parallel Decomposition for the Pi-calculus
A (fragment of a) process algebra satisfies unique parallel decomposition if
the definable behaviours admit a unique decomposition into indecomposable
parallel components. In this paper we prove that finite processes of the
pi-calculus, i.e. processes that perform no infinite executions, satisfy this
property modulo strong bisimilarity and weak bisimilarity. Our results are
obtained by an application of a general technique for establishing unique
parallel decomposition using decomposition orders.Comment: In Proceedings EXPRESS/SOS 2016, arXiv:1608.0269
A Geometric Approach to the Problem of Unique Decomposition of Processes
This paper proposes a geometric solution to the problem of prime
decomposability of concurrent processes first explored by R. Milner and F.
Moller in [MM93]. Concurrent programs are given a geometric semantics using
cubical areas, for which a unique factorization theorem is proved. An effective
factorization method which is correct and complete with respect to the
geometric semantics is derived from the factorization theorem. This algorithm
is implemented in the static analyzer ALCOOL.Comment: 15 page
Unique Decomposition of Processes
AbstractIn this paper, we examine questions about the prime decomposability of processes, where we define a process to be prime whenever it cannot be decomposed into nontrivial components.We show that any finite process can be uniquely decomposed into prime processes with respect to bisimulation equivalence, and demonstrate counterexamples to such a result for both failures (testing) equivalence and trace equivalence.Although we show that prime decompositions cannot exist for arbitrary infinite processes, we motivate but leave as open a conjecture on the unique decomposability of a wide subclass of infinite behaviours
Null flows, positive flows and the structure of stationary symmetric stable processes
This paper elucidates the connection between stationary symmetric
alpha-stable processes with 0<alpha<2 and nonsingular flows on measure spaces
by describing a new and unique decomposition of stationary stable processes
into those corresponding to positive flows and those corresponding to null
flows. We show that a necessary and sufficient for a stationary stable process
to be ergodic is that its positive component vanishes
Decomposition orders : another generalisation of the fundamental theorem of arithmetic
We discuss unique decomposition in partial commutative monoids. Inspired by a result from process theory, we propose the notion of decomposition order for partial commutative monoids, and prove that a partial commutative monoid has unique decomposition iff it can be endowed with a decomposition order. We apply our result to establish that the commutative monoid of weakly normed processes modulo bisimulation definable in ACPe with linear communication, with parallel composition as binary operation, has unique decomposition. We also apply our result to establish that the partial commutative monoid associated with a well-founded commutative residual algebra has unique decompositio
Stable stationary processes related to cyclic flows
We study stationary stable processes related to periodic and cyclic flows in
the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are
not ergodic. We provide their canonical representations, consider examples and
show how to identify them among general stationary stable processes.
We conclude with the unique decomposition in distribution of stationary
stable processes into the sum of four major independent components: 1.
A mixed moving average component. 2. A harmonizable (or ``trivial'')
component.
3. A cyclic component 4. A component which is different from these.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000010
Affine Dunkl processes
We introduce the analogue of Dunkl processes in the case of an affine root
system of type . The construction of the affine Dunkl
process is achieved by a skew-product decomposition by means of its radial part
and a jump process on the affine Weyl group, where the radial part of the
affine Dunkl process is defined as the unique solution of some stochastic
differential equation. We prove that the affine Dunkl process is a c\`adl\`ag
Markov process as well as a local martingale, study its jumps, and give a
martingale decomposition, which are properties similar to those of the
classical Dunkl process
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