2 research outputs found
Zenoness for Timed Pushdown Automata
Timed pushdown automata are pushdown automata extended with a finite set of
real-valued clocks. Additionaly, each symbol in the stack is equipped with a
value representing its age. The enabledness of a transition may depend on the
values of the clocks and the age of the topmost symbol. Therefore, dense-timed
pushdown automata subsume both pushdown automata and timed automata. We have
previously shown that the reachability problem for this model is decidable. In
this paper, we study the zenoness problem and show that it is EXPTIME-complete.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
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