134 research outputs found
Modal Logics with Hard Diamond-free Fragments
We investigate the complexity of modal satisfiability for certain
combinations of modal logics. In particular we examine four examples of
multimodal logics with dependencies and demonstrate that even if we restrict
our inputs to diamond-free formulas (in negation normal form), these logics
still have a high complexity. This result illustrates that having D as one or
more of the combined logics, as well as the interdependencies among logics can
be important sources of complexity even in the absence of diamonds and even
when at the same time in our formulas we allow only one propositional variable.
We then further investigate and characterize the complexity of the
diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers'
comments. Accepted at LFCS 201
NEXP-completeness and Universal Hardness Results for Justification Logic
We provide a lower complexity bound for the satisfiability problem of a
multi-agent justification logic, establishing that the general NEXP upper bound
from our previous work is tight. We then use a simple modification of the
corresponding reduction to prove that satisfiability for all multi-agent
justification logics from there is hard for the Sigma 2 p class of the second
level of the polynomial hierarchy - given certain reasonable conditions. Our
methods improve on these required conditions for the same lower bound for the
single-agent justification logics, proven by Buss and Kuznets in 2009, thus
answering one of their open questions.Comment: Shorter version has been accepted for publication by CSR 201
Representation of Nelson Algebras by Rough Sets Determined by Quasiorders
In this paper, we show that every quasiorder induces a Nelson algebra
such that the underlying rough set lattice is algebraic. We
note that is a three-valued {\L}ukasiewicz algebra if and only if
is an equivalence. Our main result says that if is a Nelson
algebra defined on an algebraic lattice, then there exists a set and a
quasiorder on such that .Comment: 16 page
Mechatronic system reliability evaluation using petri networks and PHI2 method
In this paper, we propose an approach allowing us to study the performance of a mechatronic system using Petri Nets in which we use particularly the PH12 method for the evaluation of failure probability of a mechanical component. The Petri Nets are used to describe the process of sequential dynamics of a system. Deterministic stochastic Petri networks have been implemented to introduce random phenomena following the laws of distribution. After the functional and dysfunctional modeling of a mechatronic system using Petri Nets, it is necessary to associate times to different transitions of the network. It is necessary to take into account a physical modeling in order to determine functional times of different components which are associated with functional transitions. Regarding dysfunctional transitions, the laws of probability are assigned depending on the knowledge concerning the reliability of different types of components: the exponential law for electronic devices, the Jelinski-Moranda model for software, etc. For the mechanical components, we use the PH12 method for the evaluation of the time variant failure probability
Functional and dysfunctional analysis of a mechatronic system
A study of system reliability is generally preceded by a functional analysis, which consists of defining the material limits, the various functions and operations realized by the system and the various configurations. This stage does not give information about the modes of failure and their effects. It is necessary to complete it by a second one taking into account the dysfunctions in order to model suitably a complex system with Petri networks. In this paper, we propose to employ SADT, FMEA, SEEA and Petri networks methods to study a mechatronic system
Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
We show that Branching-time temporal logics CTL and CTL*, as well as
Alternating-time temporal logics ATL and ATL*, are as semantically expressive
in the language with a single propositional variable as they are in the full
language, i.e., with an unlimited supply of propositional variables. It follows
that satisfiability for CTL, as well as for ATL, with a single variable is
EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a
single variable is 2EXPTIME-complete,--i.e., for these logics, the
satisfiability for formulas with only one variable is as hard as satisfiability
for arbitrary formulas.Comment: Prefinal version of the published pape
Interprocedural Reachability for Flat Integer Programs
We study programs with integer data, procedure calls and arbitrary call
graphs. We show that, whenever the guards and updates are given by octagonal
relations, the reachability problem along control flow paths within some
language w1* ... wd* over program statements is decidable in Nexptime. To
achieve this upper bound, we combine a program transformation into the same
class of programs but without procedures, with an Np-completeness result for
the reachability problem of procedure-less programs. Besides the program, the
expression w1* ... wd* is also mapped onto an expression of a similar form but
this time over the transformed program statements. Several arguments involving
context-free grammars and their generative process enable us to give tight
bounds on the size of the resulting expression. The currently existing gap
between Np-hard and Nexptime can be closed to Np-complete when a certain
parameter of the analysis is assumed to be constant.Comment: 38 pages, 1 figur
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