212,601 research outputs found
Branching cells as local states for event structures and nets: probabilistic applications
International audienceWe study the concept of choice for true concurrency models such as prime event structures and safe Petri nets. We propose a dynamic variation of the notion of cluster previously introduced for nets. This new object is defined for event structures, it is called a branching cell. Our aim is to bring an interpretation of branching cells as a right notion of “local state”, for concurrent systems. We illustrate the above claim through applications to probabilistic concurrent models. We propose a construction for probabilities over so-called locally finite event structures that makes concurrent processes probabilistically independent—simply attach a dice to each branching cell; dices attached to concurrent branching cells are thrown independently. Furthermore, we provide a true concurrency generalization of Markov chains, called Markov nets. Unlike in existing variants of stochastic Petri nets, our approach randomizes Mazurkiewicz traces, not firing sequences. We show in this context the Law of Large Numbers (LLN), which confirms that branching cells deserve the status of local state
CSP methods for identifying atomic actions in the design of fault tolerant concurrent systems
Limiting the extent of error propagation when faults occur and localizing the subsequent error recovery are common concerns in the design of fault tolerant parallel processing systems, Both activities are made easier if the designer associates fault tolerance mechanisms with the underlying atomic actions of the system, With this in mind, this paper has investigated two methods for the identification of atomic actions in parallel processing systems described using CSP, Explicit trace evaluation forms the basis of the first algorithm, which enables a designer to analyze interprocess communications and thereby locate atomic action boundaries in a hierarchical fashion, The second method takes CSP descriptions of the parallel processes and uses structural arguments to infer the atomic action boundaries. This method avoids the difficulties involved with producing full trace sets, but does incur the penalty of a more complex algorithm
Unfolding-Based Process Discovery
This paper presents a novel technique for process discovery. In contrast to
the current trend, which only considers an event log for discovering a process
model, we assume two additional inputs: an independence relation on the set of
logged activities, and a collection of negative traces. After deriving an
intermediate net unfolding from them, we perform a controlled folding giving
rise to a Petri net which contains both the input log and all
independence-equivalent traces arising from it. Remarkably, the derived Petri
net cannot execute any trace from the negative collection. The entire chain of
transformations is fully automated. A tool has been developed and experimental
results are provided that witness the significance of the contribution of this
paper.Comment: This is the unabridged version of a paper with the same title
appearead at the proceedings of ATVA 201
Event-Driven Network Programming
Software-defined networking (SDN) programs must simultaneously describe
static forwarding behavior and dynamic updates in response to events.
Event-driven updates are critical to get right, but difficult to implement
correctly due to the high degree of concurrency in networks. Existing SDN
platforms offer weak guarantees that can break application invariants, leading
to problems such as dropped packets, degraded performance, security violations,
etc. This paper introduces EVENT-DRIVEN CONSISTENT UPDATES that are guaranteed
to preserve well-defined behaviors when transitioning between configurations in
response to events. We propose NETWORK EVENT STRUCTURES (NESs) to model
constraints on updates, such as which events can be enabled simultaneously and
causal dependencies between events. We define an extension of the NetKAT
language with mutable state, give semantics to stateful programs using NESs,
and discuss provably-correct strategies for implementing NESs in SDNs. Finally,
we evaluate our approach empirically, demonstrating that it gives well-defined
consistency guarantees while avoiding expensive synchronization and packet
buffering
1-Safe Petri nets and special cube complexes: equivalence and applications
Nielsen, Plotkin, and Winskel (1981) proved that every 1-safe Petri net
unfolds into an event structure . By a result of Thiagarajan
(1996 and 2002), these unfoldings are exactly the trace regular event
structures. Thiagarajan (1996 and 2002) conjectured that regular event
structures correspond exactly to trace regular event structures. In a recent
paper (Chalopin and Chepoi, 2017, 2018), we disproved this conjecture, based on
the striking bijection between domains of event structures, median graphs, and
CAT(0) cube complexes. On the other hand, in Chalopin and Chepoi (2018) we
proved that Thiagarajan's conjecture is true for regular event structures whose
domains are principal filters of universal covers of (virtually) finite special
cube complexes.
In the current paper, we prove the converse: to any finite 1-safe Petri net
one can associate a finite special cube complex such that the
domain of the event structure (obtained as the unfolding of
) is a principal filter of the universal cover of .
This establishes a bijection between 1-safe Petri nets and finite special cube
complexes and provides a combinatorial characterization of trace regular event
structures.
Using this bijection and techniques from graph theory and geometry (MSO
theory of graphs, bounded treewidth, and bounded hyperbolicity) we disprove yet
another conjecture by Thiagarajan (from the paper with S. Yang from 2014) that
the monadic second order logic of a 1-safe Petri net is decidable if and only
if its unfolding is grid-free.
Our counterexample is the trace regular event structure
which arises from a virtually special square complex . The domain of
is grid-free (because it is hyperbolic), but the MSO
theory of the event structure is undecidable
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