186 research outputs found
Optimal Tableaux Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-time Temporal Logic ATL+
We develop a sound, complete and practically implementable tableaux-based
decision method for constructive satisfiability testing and model synthesis in
the fragment ATL+ of the full Alternating time temporal logic ATL*. The method
extends in an essential way a previously developed tableaux-based decision
method for ATL and works in 2EXPTIME, which is the optimal worst case
complexity of the satisfiability problem for ATL+ . We also discuss how
suitable parametrizations and syntactic restrictions on the class of input ATL+
formulae can reduce the complexity of the satisfiability problem.Comment: 45 page
Naturally occurring polyphenols as building blocks for supramolecular liquid crystals-substitution pattern dominates mesomorphism
A modular supramolecular approach towards hydrogen-bonded liquid crystalline assemblies based on naturally occurring polyphenols is reported. The combination of experimental observations, crystallographic studies and semi-empirical analyses of the assemblies provides insight into the structure-property relationships of these materials. Here a direct correlation of the number of donor OH-groups as well as their orientation with the mesomorphic behavior is reported. We discovered that the number and orientation of the OH-groups have a stronger influence on the mesomorphic behavior of the supramolecular assemblies than the connectivity (e.g. stilbenoid or chalconoid) of the hydrogen bond donors. Furthermore, the photo-switching behavior of selected complexes containing azopyridine ligands was investigated. This study will help future scientists to gain a deeper understanding of the underlying mechanisms and structure-property relationships of supramolecular assemblies with mesomorphic behavior, which is still one of the major challenges in current scienc
An Improvement of the Piggyback Algorithm for Parallel Model Checking
This paper extends the piggyback algorithm to enlarge the set of liveness properties it can verify. Its extension is motivated by an attempt to express in logic the counterexamples it can detect and relate them to bounded liveness. The original algorithm is based on parallel breadth-first search and piggybacking of accepting states that are deleted after counting a fixed number of transitions. The main improvement is obtained by renewing the counter of transitions when the same accepting states are visited in the negated property automaton. In addition, we describe piggybacking of multiple states in either sets (exact) or Bloom filters (lossy but conservative), and use of local searches that attempt to connect cycles fragmented among processing cores. Finally it is proved that accepting cycle detection is in NC in the size of the product automaton's entire state space, including unreachable states
The nil Hecke ring and singularity of Schubert varieties
We give a criterion for smoothness of a point in any Schubert variety in any
G/B in terms of the nil Hecke ring.Comment: AMSTE
On the Sets of Real Numbers Recognized by Finite Automata in Multiple Bases
This article studies the expressive power of finite automata recognizing sets
of real numbers encoded in positional notation. We consider Muller automata as
well as the restricted class of weak deterministic automata, used as symbolic
set representations in actual applications. In previous work, it has been
established that the sets of numbers that are recognizable by weak
deterministic automata in two bases that do not share the same set of prime
factors are exactly those that are definable in the first order additive theory
of real and integer numbers. This result extends Cobham's theorem, which
characterizes the sets of integer numbers that are recognizable by finite
automata in multiple bases.
In this article, we first generalize this result to multiplicatively
independent bases, which brings it closer to the original statement of Cobham's
theorem. Then, we study the sets of reals recognizable by Muller automata in
two bases. We show with a counterexample that, in this setting, Cobham's
theorem does not generalize to multiplicatively independent bases. Finally, we
prove that the sets of reals that are recognizable by Muller automata in two
bases that do not share the same set of prime factors are exactly those
definable in the first order additive theory of real and integer numbers. These
sets are thus also recognizable by weak deterministic automata. This result
leads to a precise characterization of the sets of real numbers that are
recognizable in multiple bases, and provides a theoretical justification to the
use of weak automata as symbolic representations of sets.Comment: 17 page
A unified approach on Springer fibers in the hook, two-row and two-column cases
We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan
basis and consider the standard torus relative to this. We deal with the
problem to describe the flags fixed by the torus which belong to a given
component of the Springer fiber. We solve the problem in the hook, two-row and
two-column cases. We provide two main characterizations which are common to the
three cases, and which involve dominance relations between Young diagrams and
combinatorial algorithms. Then, for these three cases, we deduce topological
properties of the components and their intersections.Comment: 42 page
A theory of normed simulations
In existing simulation proof techniques, a single step in a lower-level
specification may be simulated by an extended execution fragment in a
higher-level one. As a result, it is cumbersome to mechanize these techniques
using general purpose theorem provers. Moreover, it is undecidable whether a
given relation is a simulation, even if tautology checking is decidable for the
underlying specification logic. This paper introduces various types of normed
simulations. In a normed simulation, each step in a lower-level specification
can be simulated by at most one step in the higher-level one, for any related
pair of states. In earlier work we demonstrated that normed simulations are
quite useful as a vehicle for the formalization of refinement proofs via
theorem provers. Here we show that normed simulations also have pleasant
theoretical properties: (1) under some reasonable assumptions, it is decidable
whether a given relation is a normed forward simulation, provided tautology
checking is decidable for the underlying logic; (2) at the semantic level,
normed forward and backward simulations together form a complete proof method
for establishing behavior inclusion, provided that the higher-level
specification has finite invisible nondeterminism.Comment: 31 pages, 10figure
Formal methods and tools for the development of distributed and real time systems : Esprit Project 3096 (SPEC)
The Basic Research Action No. 3096, Formal Methods snd Tools for the Development of Distributed and Real Time Systems, is funded in the Area of Computer Science, under the ESPRIT Programme of the European Community. The coordinating institution is the Department of Computing Science, Eindhoven University of Technology, and the participating Institutions are the Institute of Computer Science of Crete. the Swedish Institute of Computer Science, the Programmimg Research Group of the University of Oxford, and the Computer Science Departments of the University of Manchester, Imperial
College. Weizmann Institute of Science, Eindhoven University of Technology, IMAG Grenoble. Catholic University of Nijmegen, and the University of Liege. This document contains the synopsis. and part of the sections on objectives and area of advance, on baseline and rationale, on research goals, and on organisation of the action, as contained in the original proposal, submitted June, 198S. The section on the state of the art (18 pages) and the full list of references (21 pages) of the original proposal have been deleted because of limitation of available space
Propositional Dynamic Logic for Message-Passing Systems
We examine a bidirectional propositional dynamic logic (PDL) for finite and
infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of
multi-modal logic we can express properties both in the entire future and in
the past of an event. Path expressions strengthen the classical until operator
of temporal logic. For every formula defining an MSC language, we construct a
communicating finite-state machine (CFM) accepting the same language. The CFM
obtained has size exponential in the size of the formula. This synthesis
problem is solved in full generality, i.e., also for MSCs with unbounded
channels. The model checking problem for CFMs and HMSCs turns out to be in
PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with
intersection, the semantics of a formula cannot be captured by a CFM anymore
Robust Model-Checking of Linear-Time Properties in Timed Automata
International audienceFormal verification of timed systems is well understood, but their \emphimplementation is still challenging. Recent works by Raskin \emphet al. have brought out a model of parameterized timed automata that can be used to prove \emphimplementability of timed systems for safety properties. We define here a more general notion of robust model-checking for linear-time properties, which consists in verifying whether a property still holds even if the transitions are slightly delayed or expedited. We provide PSPACE algorithms for the robust model-checking of Büchi-like and LTL properties. We also verify bounded-response-time properties
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