7 research outputs found
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
Computing Optimal Coverability Costs in Priced Timed Petri Nets
We consider timed Petri nets, i.e., unbounded Petri nets where each token
carries a real-valued clock. Transition arcs are labeled with time intervals,
which specify constraints on the ages of tokens. Our cost model assigns token
storage costs per time unit to places, and firing costs to transitions. We
study the cost to reach a given control-state. In general, a cost-optimal run
may not exist. However, we show that the infimum of the costs is computable.Comment: 26 pages. Contribution to LICS 201
On Supervisory Policies that Enforce Liveness in Partially Controlled Free-Choice Petri Nets
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryItem is misnumbered as UILU-ENG-2205National Science Foundation / ECS-0426831, CNS-0437415, and CNS-083440
Dense-Timed Petri Nets: Checking Zenoness, Token liveness and Boundedness
We consider Dense-Timed Petri Nets (TPN), an extension of Petri nets in which
each token is equipped with a real-valued clock and where the semantics is lazy
(i.e., enabled transitions need not fire; time can pass and disable
transitions). We consider the following verification problems for TPNs. (i)
Zenoness: whether there exists a zeno-computation from a given marking, i.e.,
an infinite computation which takes only a finite amount of time. We show
decidability of zenoness for TPNs, thus solving an open problem from [Escrig et
al.]. Furthermore, the related question if there exist arbitrarily fast
computations from a given marking is also decidable. On the other hand,
universal zenoness, i.e., the question if all infinite computations from a
given marking are zeno, is undecidable. (ii) Token liveness: whether a token is
alive in a marking, i.e., whether there is a computation from the marking which
eventually consumes the token. We show decidability of the problem by reducing
it to the coverability problem, which is decidable for TPNs. (iii) Boundedness:
whether the size of the reachable markings is bounded. We consider two versions
of the problem; namely semantic boundedness where only live tokens are taken
into consideration in the markings, and syntactic boundedness where also dead
tokens are considered. We show undecidability of semantic boundedness, while we
prove that syntactic boundedness is decidable through an extension of the
Karp-Miller algorithm.Comment: 61 pages, 18 figure