200 research outputs found
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
Well Structured Transition Systems with History
We propose a formal model of concurrent systems in which the history of a
computation is explicitly represented as a collection of events that provide a
view of a sequence of configurations. In our model events generated by
transitions become part of the system configurations leading to operational
semantics with historical data. This model allows us to formalize what is
usually done in symbolic verification algorithms. Indeed, search algorithms
often use meta-information, e.g., names of fired transitions, selected
processes, etc., to reconstruct (error) traces from symbolic state exploration.
The other interesting point of the proposed model is related to a possible new
application of the theory of well-structured transition systems (wsts). In our
setting wsts theory can be applied to formally extend the class of properties
that can be verified using coverability to take into consideration (ordered and
unordered) historical data. This can be done by using different types of
representation of collections of events and by combining them with wsts by
using closure properties of well-quasi orderings.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Adding Time to Pushdown Automata
In this tutorial, we illustrate through examples how we can combine two
classical models, namely those of pushdown automata (PDA) and timed automata,
in order to obtain timed pushdown automata (TPDA). Furthermore, we describe how
the reachability problem for TPDAs can be reduced to the reachability problem
for PDAs.Comment: In Proceedings QFM 2012, arXiv:1212.345
Sampled Semantics of Timed Automata
Sampled semantics of timed automata is a finite approximation of their dense
time behavior. While the former is closer to the actual software or hardware
systems with a fixed granularity of time, the abstract character of the latter
makes it appealing for system modeling and verification. We study one aspect of
the relation between these two semantics, namely checking whether the system
exhibits some qualitative (untimed) behaviors in the dense time which cannot be
reproduced by any implementation with a fixed sampling rate. More formally, the
\emph{sampling problem} is to decide whether there is a sampling rate such that
all qualitative behaviors (the untimed language) accepted by a given timed
automaton in dense time semantics can be also accepted in sampled semantics. We
show that this problem is decidable
Decisive Markov Chains
We consider qualitative and quantitative verification problems for
infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given
set of target states F if it almost certainly eventually reaches either F or a
state from which F can no longer be reached. While all finite Markov chains are
trivially decisive (for every set F), this also holds for many classes of
infinite Markov chains. Infinite Markov chains which contain a finite attractor
are decisive w.r.t. every set F. In particular, this holds for probabilistic
lossy channel systems (PLCS). Furthermore, all globally coarse Markov chains
are decisive. This class includes probabilistic vector addition systems (PVASS)
and probabilistic noisy Turing machines (PNTM). We consider both safety and
liveness problems for decisive Markov chains, i.e., the probabilities that a
given set of states F is eventually reached or reached infinitely often,
respectively. 1. We express the qualitative problems in abstract terms for
decisive Markov chains, and show an almost complete picture of its decidability
for PLCS, PVASS and PNTM. 2. We also show that the path enumeration algorithm
of Iyer and Narasimha terminates for decisive Markov chains and can thus be
used to solve the approximate quantitative safety problem. A modified variant
of this algorithm solves the approximate quantitative liveness problem. 3.
Finally, we show that the exact probability of (repeatedly) reaching F cannot
be effectively expressed (in a uniform way) in Tarski-algebra for either PLCS,
PVASS or (P)NTM.Comment: 32 pages, 0 figure
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
Canonized Rewriting and Ground AC Completion Modulo Shostak Theories : Design and Implementation
AC-completion efficiently handles equality modulo associative and commutative
function symbols. When the input is ground, the procedure terminates and
provides a decision algorithm for the word problem. In this paper, we present a
modular extension of ground AC-completion for deciding formulas in the
combination of the theory of equality with user-defined AC symbols,
uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. Our
algorithm, called AC(X), is obtained by augmenting in a modular way ground
AC-completion with the canonizer and solver present for the theory X. This
integration rests on canonized rewriting, a new relation reminiscent to
normalized rewriting, which integrates canonizers in rewriting steps. AC(X) is
proved sound, complete and terminating, and is implemented to extend the core
of the Alt-Ergo theorem prover.Comment: 30 pages, full version of the paper TACAS'11 paper "Canonized
Rewriting and Ground AC-Completion Modulo Shostak Theories" accepted for
publication by LMCS (Logical Methods in Computer Science
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
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