31 research outputs found
Integer Vector Addition Systems with States
This paper studies reachability, coverability and inclusion problems for
Integer Vector Addition Systems with States (ZVASS) and extensions and
restrictions thereof. A ZVASS comprises a finite-state controller with a finite
number of counters ranging over the integers. Although it is folklore that
reachability in ZVASS is NP-complete, it turns out that despite their
naturalness, from a complexity point of view this class has received little
attention in the literature. We fill this gap by providing an in-depth analysis
of the computational complexity of the aforementioned decision problems. Most
interestingly, it turns out that while the addition of reset operations to
ordinary VASS leads to undecidability and Ackermann-hardness of reachability
and coverability, respectively, they can be added to ZVASS while retaining
NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure
Decision Problems for Petri Nets with Names
We prove several decidability and undecidability results for nu-PN, an
extension of P/T nets with pure name creation and name management. We give a
simple proof of undecidability of reachability, by reducing reachability in
nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly
surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition
Systems. In particular, we obtain decidability of coverability and termination,
so that the expressive power of Turing machines is not reached. Moreover, they
are strictly Well Structured, so that the boundedness problem is also
decidable. We consider two properties, width-boundedness and depth-boundedness,
that factorize boundedness. Width-boundedness has already been proven to be
decidable. We prove here undecidability of depth-boundedness. Finally, we
obtain Ackermann-hardness results for all our decidable decision problems.Comment: 20 pages, 7 figure
Π‘Π΅ΡΠΈ Π°ΠΊΡΠΈΠ²Π½ΡΡ ΡΠ΅ΡΡΡΡΠΎΠ²
In this work nets of active resources (AR-nets) are presented. This is a generalization of Petri nets (ordinary and Super-dual) with a single type of nodes and two types of arcs (consuming and producing). Each node may contain a number of tokens (resources), that can be consumed or produced by "firings" of other tokens (location of consumed/produced resources is defined by corresponding arcs). So, in this model the same token may be considered as a passive resource (produced or consumed by agents) and an active agent (producing or consuming resources) at the same time.
The expressive power of AR-nets and two modified models is studied. It is shown, that AR-nets and AR-nets with simple firing are equivalent to ordinary Petri nets. AR-nets with simultaneous firing are strictly more expressive.ΠΠ²ΠΎΠ΄ΠΈΡΡΡ ΡΠΎΡΠΌΠ°Π»ΠΈΠ·ΠΌ ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ, Π½Π°Π·Π²Π°Π½Π½ΡΠΉ ΡΠ΅ΡΡΠΌΠΈ Π°ΠΊΡΠΈΠ²Π½ΡΡ
ΡΠ΅ΡΡΡΡΠΎΠ². Π€ΠΎΡΠΌΠ°Π»ΠΈΠ·ΠΌ ΠΏΠΎΡΡΡΠΎΠ΅Π½ ΠΊΠ°ΠΊ ΠΎΠ±ΠΎΠ±ΡΠ΅Π½ΠΈΠ΅ ΡΠ΅ΡΠ΅ΠΉ ΠΠ΅ΡΡΠΈ, Π² ΠΊΠΎΡΠΎΡΠΎΠΌ ΡΠ±ΡΠ°Π½ΠΎ ΡΠ°Π·Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠΎΠ² ΡΠΈΡΡΠ΅ΠΌΡ Π½Π° Π°ΠΊΡΠΈΠ²Π½ΡΠ΅ ΠΈ ΠΏΠ°ΡΡΠΈΠ²Π½ΡΠ΅ (ΠΏΠ΅ΡΠ΅Ρ
ΠΎΠ΄Ρ ΠΈ ΠΏΠΎΠ·ΠΈΡΠΈΠΈ). ΠΠ°ΠΆΠ΄ΡΠΉ ΡΠ΅ΡΡΡΡ (ΠΌΠ°ΡΠΊΠ΅Ρ ΡΠ·Π»Π° ΡΠ΅ΡΠΈ) ΠΌΠΎΠΆΠ΅Ρ Π²ΡΡΡΡΠΏΠ°ΡΡ ΠΈ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΏΠ°ΡΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠ΅ΡΡΡΡΠ°, ΠΏΠΎΡΡΠ΅Π±Π»ΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΈΠ»ΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΠΌΠΎΠ³ΠΎ Π΄ΡΡΠ³ΠΈΠΌΠΈ Π°Π³Π΅Π½ΡΠ°ΠΌΠΈ, ΠΈ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π°Π³Π΅Π½ΡΠ°, ΠΏΠΎΡΡΠ΅Π±Π»ΡΡΡΠ΅Π³ΠΎ ΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ΅Π³ΠΎ Π΄ΡΡΠ³ΠΈΠ΅ ΡΠ΅ΡΡΡΡΡ
ΠΡΠΎΡΡΠΎΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΏΠΎΠΊΡΡΡΠΈΡ Π΄Π»Ρ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΡ ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ ΡΠΈΡΡΠ΅ΠΌ
An algorithm for solving the coverability problem for monotonic counter systems is presented. The solvability of this problem is well-known, but the algorithm is interesting due to its simplicity. The algorithm has emerged as a simplification of a certain procedure of a supercompiler application (a program specializer based on V.F. Turchin's supercompilation) to a program encoding a monotonic counter system along with initial and target sets of states and from the proof that under some conditions the procedure terminates and solves the coverability problem.ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°Π΄Π°ΡΠΈ ΠΏΠΎΠΊΡΡΡΠΈΡ Π΄Π»Ρ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΡ
ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ
ΡΠΈΡΡΠ΅ΠΌ. Π Π°Π·ΡΠ΅ΡΠΈΠΌΠΎΡΡΡ ΡΡΠΎΠΉ Π·Π°Π΄Π°ΡΠΈ Ρ
ΠΎΡΠΎΡΠΎ ΠΈΠ·Π²Π΅ΡΡΠ½Π°, Π½ΠΎ Π΄Π°Π½Π½ΡΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΠΈΠ½ΡΠ΅ΡΠ΅ΡΠ΅Π½ ΡΠ²ΠΎΠ΅ΠΉ ΠΏΡΠΎΡΡΠΎΡΠΎΠΉ. ΠΠ½ Π²ΠΎΠ·Π½ΠΈΠΊ ΠΈΠ· ΡΠΏΡΠΎΡΠ΅Π½ΠΈΡ Π½Π΅ΠΊΠΎΡΠΎΡΠΎΠΉ ΠΈΡΠ΅ΡΠ°ΡΠΈΠ²Π½ΠΎΠΉ ΠΏΡΠΎΡΠ΅Π΄ΡΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΡΠΏΠ΅ΡΠΊΠΎΠΌΠΏΠΈΠ»ΡΡΠΎΡΠ° (ΡΠΏΠ΅ΡΠΈΠ°Π»ΠΈΠ·Π°ΡΠΎΡΠ° ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌ, ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ Π½Π° ΠΌΠ΅ΡΠΎΠ΄Π΅ ΡΡΠΏΠ΅ΡΠΊΠΎΠΌΠΏΠΈΠ»ΡΡΠΈΠΈ Π.Π€. Π’ΡΡΡΠΈΠ½Π°) ΠΊ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ΅, ΠΊΠΎΠ΄ΠΈΡΡΡΡΠ΅ΠΉ ΡΡΠ΅ΡΡΠΈΠΊΠΎΠ²ΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΠΈ Π½Π°ΡΠ°Π»ΡΠ½ΠΎΠ΅ ΠΈ ΡΠ΅Π»Π΅Π²ΠΎΠ΅ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π° ΡΠΎΡΡΠΎΡΠ½ΠΈΠΉ, ΠΈ ΠΈΠ· Π΄ΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΡΡΠ²Π°, ΡΡΠΎ ΠΏΡΠΈ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΡΡΠ° ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ° Π·Π°Π²Π΅ΡΡΠ°Π΅ΡΡΡ ΠΈ ΡΠ΅ΡΠ°Π΅Ρ Π·Π°Π΄Π°ΡΡ ΠΏΠΎΠΊΡΡΡΠΈΡ
Incremental, Inductive Coverability
We give an incremental, inductive (IC3) procedure to check coverability of
well-structured transition systems. Our procedure generalizes the IC3 procedure
for safety verification that has been successfully applied in finite-state
hardware verification to infinite-state well-structured transition systems. We
show that our procedure is sound, complete, and terminating for downward-finite
well-structured transition systems---where each state has a finite number of
states below it---a class that contains extensions of Petri nets, broadcast
protocols, and lossy channel systems.
We have implemented our algorithm for checking coverability of Petri nets. We
describe how the algorithm can be efficiently implemented without the use of
SMT solvers. Our experiments on standard Petri net benchmarks show that IC3 is
competitive with state-of-the-art implementations for coverability based on
symbolic backward analysis or expand-enlarge-and-check algorithms both in time
taken and space usage.Comment: Non-reviewed version, original version submitted to CAV 2013; this is
a revised version, containing more experimental results and some correction
The Well Structured Problem for Presburger Counter Machines
International audienceWe introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter machines except for Affine VASS of dimension one. However, the strong well structured problem is decidable for all Presburger counter machines. While Affine VASS of dimension one are not, in general, well structured, we give an algorithm that computes the set of predecessors of a configuration; as a consequence this allows to decide the well structured problem for 1-Affine VASS
A modelling approach for railway overhead line equipment asset management
The Overhead Line Equipment (OLE) is a critical sub-system of the 25kV AC overhead railway electrification system. If OLE asset management strategies can be evaluated using a whole lifecycle cost analysis that considers degradation processes and maintenance activities of the OLE components, the investment required to deliver the level of performance desired by railway customers and regulators can be based on evidence from the analysis results. A High Level Petri Net (HLPN) model, proposed in this paper, is used to simulate the degradation, failure, inspection and maintenance of the main OLE components and to calculate various statistics, associated with the cost and reliability of the system over its lifecycle. The HLPN considers all the main OLE components in a single model and it can simulate fixed frequency inspections and condition-based maintenance regimes. In order to allow the relevant processes to be modelled accurately and efficiently, the HLPN features are used, such as specific data about individual components is taken account of in the general model. The HLPN, developed using international standards, is described in detail and a framework of its analysis for reliability and lifecycle cost evaluation is proposed. In this novel whole system model different OLE component types and their instances on a line are modelled simultaneously, and the dependencies are considered in terms of opportunistic inspection and maintenance. An example HLPN for the catenary wire is used to illustrate the model, and an application of the methodology for whole lifecycle cost evaluation of a two-mile OLE line is presented
Forward Analysis for WSTS, Part III: Karp-Miller Trees
This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions"
[STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and "Forward Analysis
for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3),
2012]. In these two papers, we provided a framework to conduct forward
reachability analyses of WSTS, using finite representations of downward-closed
sets. We further develop this framework to obtain a generic Karp-Miller
algorithm for the new class of very-WSTS. This allows us to show that
coverability sets of very-WSTS can be computed as their finite ideal
decompositions. Under natural effectiveness assumptions, we also show that LTL
model checking for very-WSTS is decidable. The termination of our procedure
rests on a new notion of acceleration levels, which we study. We characterize
those domains that allow for only finitely many accelerations, based on ordinal
ranks