4,042 research outputs found
Minimal Coverability Set for Petri Nets: Karp and Miller Algorithm with Pruning
This paper presents the Monotone-Pruning algorithm (MP) for computing the minimal coverability set of Petri nets. The original Karp and Miller algorithm (K&M) unfolds the reachability graph of a Petri net and uses acceleration on branches to ensure termination. The MP algorithm improves the K&M algorithm by adding pruning between branches of the K&M tree. This idea was first introduced in the Minimal Coverability Tree algorithm (MCT), however it was recently shown to be incomplete. The MP algorithm can be viewed as the MCT algorithm with a slightly more aggressive pruning strategy which ensures completeness. Experimental results show that this algorithm is a strong improvement over the K&M algorithm as it dramatically reduces the exploration tree
Quasi-exactly Solvable Lie Superalgebras of Differential Operators
In this paper, we study Lie superalgebras of matrix-valued
first-order differential operators on the complex line. We first completely
classify all such superalgebras of finite dimension. Among the
finite-dimensional superalgebras whose odd subspace is nontrivial, we find
those admitting a finite-dimensional invariant module of smooth vector-valued
functions, and classify all the resulting finite-dimensional modules. The
latter Lie superalgebras and their modules are the building blocks in the
construction of QES quantum mechanical models for spin 1/2 particles in one
dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page
Quasi-Exactly Solvable Spin 1/2 Schr\"odinger Operators
The algebraic structures underlying quasi-exact solvability for spin 1/2
Hamiltonians in one dimension are studied in detail. Necessary and sufficient
conditions for a matrix second-order differential operator preserving a space
of wave functions with polynomial components to be equivalent to a \sch\
operator are found. Systematic simplifications of these conditions are
analyzed, and are then applied to the construction of several new examples of
multi-parameter QES spin 1/2 Hamiltonians in one dimension.Comment: 32 pages, LaTeX2e using AMS-LaTeX packag
On form-preserving transformations for the time-dependent Schr\"odinger equation
In this paper we point out a close connection between the Darboux
transformation and the group of point transformations which preserve the form
of the time-dependent Schr\"odinger equation (TDSE). In our main result, we
prove that any pair of time-dependent real potentials related by a Darboux
transformation for the TDSE may be transformed by a suitable point
transformation into a pair of time-independent potentials related by a usual
Darboux transformation for the stationary Schr\"odinger equation. Thus, any
(real) potential solvable via a time-dependent Darboux transformation can
alternatively be solved by applying an appropriate form-preserving
transformation of the TDSE to a time-independent potential. The preeminent role
of the latter type of transformations in the solution of the TDSE is
illustrated with a family of quasi-exactly solvable time-dependent anharmonic
potentials.Comment: LaTeX2e (with amsmath, amssymb, amscd, cite packages), 11 page
Exchange operator formalism for N-body spin models with near-neighbors interactions
We present a detailed analysis of the spin models with near-neighbors
interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214]
by a suitable generalization of the exchange operator formalism. We provide a
complete description of a certain flag of finite-dimensional spaces of spin
functions preserved by the Hamiltonian of each model. By explicitly
diagonalizing the Hamiltonian in the latter spaces, we compute several infinite
families of eigenfunctions of the above models in closed form in terms of
generalized Laguerre and Jacobi polynomials.Comment: RevTeX, 31 pages, no figures; important additional conten
Using a Combination of Micro-Computed Tomography, CAD and 3D Printing Techniques to Reconstruct Incomplete 19th-Century Cantonese Chess Pieces
Approaching the Coverability Problem Continuously
The coverability problem for Petri nets plays a central role in the
verification of concurrent shared-memory programs. However, its high
EXPSPACE-complete complexity poses a challenge when encountered in real-world
instances. In this paper, we develop a new approach to this problem which is
primarily based on applying forward coverability in continuous Petri nets as a
pruning criterion inside a backward coverability framework. A cornerstone of
our approach is the efficient encoding of a recently developed polynomial-time
algorithm for reachability in continuous Petri nets into SMT. We demonstrate
the effectiveness of our approach on standard benchmarks from the literature,
which shows that our approach decides significantly more instances than any
existing tool and is in addition often much faster, in particular on large
instances.Comment: 18 pages, 4 figure
Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations
We introduce a new class of graph transformation systems in which rewrite
rules can be guarded by universally quantified conditions on the neighbourhood
of nodes. These conditions are defined via special graph patterns which may be
transformed by the rule as well. For the new class for graph rewrite rules, we
provide a symbolic procedure working on minimal representations of upward
closed sets of configurations. We prove correctness and effectiveness of the
procedure by a categorical presentation of rewrite rules as well as the
involved order, and using results for well-structured transition systems. We
apply the resulting procedure to the analysis of the Distributed Dining
Philosophers protocol on an arbitrary network structure.Comment: Extended version of a submittion accepted at RP'14 Worksho
Single Versus Concurrent Systems: Nominal Classification in Mian
The Papuan language Mian allows us to refine the typology of nominal classification. Mian has two candidate classification systems, differing completely in their formal realization but overlapping considerably in their semantics. To determine whether to analyse Mian as a single system or concurrent systems we adopt a canonical approach. Our criteria – orthogonality of the systems (we give a precise measure), semantic compositionality, morphosyntactic alignment, distribution across parts of speech, exponence, and interaction with other features – point mainly to an analysis as concurrent systems. We thus improve our analysis of Mian and make progress with the typology of nominal classification
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
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