105 research outputs found
On Pebble Automata for Data Languages with Decidable Emptiness Problem
In this paper we study a subclass of pebble automata (PA) for data languages
for which the emptiness problem is decidable. Namely, we introduce the
so-called top view weak PA. Roughly speaking, top view weak PA are weak PA
where the equality test is performed only between the data values seen by the
two most recently placed pebbles. The emptiness problem for this model is
decidable. We also show that it is robust: alternating, nondeterministic and
deterministic top view weak PA have the same recognition power. Moreover, this
model is strong enough to accept all data languages expressible in Linear
Temporal Logic with the future-time operators, augmented with one register
freeze quantifier.Comment: An extended abstract of this work has been published in the
proceedings of the 34th International Symposium on Mathematical Foundations
of Computer Science (MFCS) 2009}, Springer, Lecture Notes in Computer Science
5734, pages 712-72
On the index of Simon's congruence for piecewise testability
© 2014 Elsevier B.V. Simon's congruence, denoted by ∼ n , relates words having the same subwords of length up to n. We show that, over a k-letter alphabet, the number of words modulo ∼ n is in 2 Θ (n k-1 lognθ)
К вопросу об оценке противокоррозионной эффективности ингибиторов атмосферной коррозии
Розробка, дослідження захисних антикорозійних властивостей і визначення механізму дії інгібіторів атмосферної корозії, призначених для захисту металу з тонкими шарами іржі, потребує проведення натурних та прискорених корозійних випробувань. Оскільки у більшості випадків цей процес довготривалий, то для швидкого визначення антикорозійної ефективності інгібіторів корозії розроблена методика їх прискорених випробувань. Методика полягає у визначенні захисних властивостей інгібітору шляхом зняття поляризаційних кривих у нейтральному середовищі на металі з продуктами атмосферної корозії та захисною плівкою.Development, research of protective anticorrosive properties and determination of mechanism of action of atmospheric corrosion inhibitors for the protection of metal with thin layers of rust demands carrying out of the natural and accelerated corrosion tests. As in most cases this process long, for rapid determination of anticorrosive efficiency of corrosion inhibitors the new method of their accelerated tests is developed. A method consists in definition of protective ability by removal of polarization curves on a metal with the products of atmospheric corrosion and protective film in a neutral environment
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
The ideal view on Rackoff's coverability technique
Rackoff’s small witness property for the coverability problem is the standard means to prove tight upper bounds in vector addition systems (VAS) and many extensions. We show how to derive the same bounds directly on the computations of the VAS instantiation of the generic backward coverability algorithm. This relies on a dual view of the algorithm using ideal decompositions of downwards-closed sets, which exhibits a key structural invariant in the VAS case. The same reasoning readily generalises to several VAS extensions
Kleene Algebras and Semimodules for Energy Problems
With the purpose of unifying a number of approaches to energy problems found
in the literature, we introduce generalized energy automata. These are finite
automata whose edges are labeled with energy functions that define how energy
levels evolve during transitions. Uncovering a close connection between energy
problems and reachability and B\"uchi acceptance for semiring-weighted
automata, we show that these generalized energy problems are decidable. We also
provide complexity results for important special cases
Parameterized Verification of Safety Properties in Ad Hoc Network Protocols
We summarize the main results proved in recent work on the parameterized
verification of safety properties for ad hoc network protocols. We consider a
model in which the communication topology of a network is represented as a
graph. Nodes represent states of individual processes. Adjacent nodes represent
single-hop neighbors. Processes are finite state automata that communicate via
selective broadcast messages. Reception of a broadcast is restricted to
single-hop neighbors. For this model we consider a decision problem that can be
expressed as the verification of the existence of an initial topology in which
the execution of the protocol can lead to a configuration with at least one
node in a certain state. The decision problem is parametric both on the size
and on the form of the communication topology of the initial configurations. We
draw a complete picture of the decidability and complexity boundaries of this
problem according to various assumptions on the possible topologies.Comment: In Proceedings PACO 2011, arXiv:1108.145
Crime in Maine 2014
Automata over infinite alphabets have recently come to be studied extensively
as potentially useful tools for solving problems in verification and database
theory. One popular model of automata studied is the Class Memory Automata
(CMA), for which the emptiness problem is equivalent to Petri Net Reachability.
We identify a restriction - which we call weakness - of CMA, and show that
their emptiness problem is equivalent to Petri Net Coverability. Further, we
show that in the deterministic case they are closed under all Boolean
operations. We clarify the connections between weak CMA and existing automata
over data languages. We also extend CMA to operate over multiple levels of
nested data values, and show that while these have undecidable emptiness in
general, adding the weakness constraint recovers decidability of emptiness, via
reduction to coverability in well-structured transition systems. We also
examine connections with existing automata over nested data.Comment: Preprint of LATA'15 pape
On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems
We prove a general finite convergence theorem for "upward-guarded" fixpoint
expressions over a well-quasi-ordered set. This has immediate applications in
regular model checking of well-structured systems, where a main issue is the
eventual convergence of fixpoint computations. In particular, we are able to
directly obtain several new decidability results on lossy channel systems.Comment: 16 page
Interval temporal logic model checking: The border between good and bad HS fragments
The model checking problem has thoroughly been explored in the context of standard point-based temporal logics, such as LTL, CTL, and CTL 17, whereas model checking for interval temporal logics has been brought to the attention only very recently. In this paper, we prove that the model checking problem for the logic of Allen\u2019s relations started-by and finished-by is highly intractable, as it can be proved to be EXPSPACE-hard. Such a lower bound immediately propagates to the full Halpern and Shoham\u2019s modal logic of time intervals (HS). In contrast, we show that other noteworthy HS fragments, namely, Propositional Neighbourhood Logic extended with modalities for the Allen relation starts (resp., finishes) and its inverse started-by (resp., finished-by), turn out to have\u2014maybe unexpectedly\u2014the same complexity as LTL (i.e., they are PSPACE-complete), thus joining the group of other already studied, well-behaved albeit less expressive, HS fragments
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