69,809 research outputs found
Computation Tree Logic with Deadlock Detection
We study the equivalence relation on states of labelled transition systems of
satisfying the same formulas in Computation Tree Logic without the next state
modality (CTL-X). This relation is obtained by De Nicola & Vaandrager by
translating labelled transition systems to Kripke structures, while lifting the
totality restriction on the latter. They characterised it as divergence
sensitive branching bisimulation equivalence.
We find that this equivalence fails to be a congruence for interleaving
parallel composition. The reason is that the proposed application of CTL-X to
non-total Kripke structures lacks the expressiveness to cope with deadlock
properties that are important in the context of parallel composition. We
propose an extension of CTL-X, or an alternative treatment of non-totality,
that fills this hiatus. The equivalence induced by our extension is
characterised as branching bisimulation equivalence with explicit divergence,
which is, moreover, shown to be the coarsest congruence contained in divergence
sensitive branching bisimulation equivalence
Primitive Words, Free Factors and Measure Preservation
Let F_k be the free group on k generators. A word w \in F_k is called
primitive if it belongs to some basis of F_k. We investigate two criteria for
primitivity, and consider more generally, subgroups of F_k which are free
factors.
The first criterion is graph-theoretic and uses Stallings core graphs: given
subgroups of finite rank H \le J \le F_k we present a simple procedure to
determine whether H is a free factor of J. This yields, in particular, a
procedure to determine whether a given element in F_k is primitive.
Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from
the direct product of k copies of G to G), where G is an arbitrary finite
group. We call w measure preserving if given uniform measure on G x G x ... x
G, w induces uniform measure on G (for every finite G). This is the second
criterion we investigate: it is not hard to see that primitivity implies
measure preservation and it was conjectured that the two properties are
equivalent. Our combinatorial approach to primitivity allows us to make
progress on this problem and in particular prove the conjecture for k=2.
It was asked whether the primitive elements of F_k form a closed set in the
profinite topology of free groups. Our results provide a positive answer for
F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I:
A New Algorithm", and "On Primitive Words II: Measure Preservation". 42
pages, 14 figures. Some parts of the paper reorganized towards publication in
the Israel J. of Mat
A Topology-Preserving Level Set Method for Shape Optimization
The classical level set method, which represents the boundary of the unknown
geometry as the zero-level set of a function, has been shown to be very
effective in solving shape optimization problems. The present work addresses
the issue of using a level set representation when there are simple geometrical
and topological constraints. We propose a logarithmic barrier penalty which
acts to enforce the constraints, leading to an approximate solution to shape
design problems.Comment: 10 pages, 4 figure
Recovering Grammar Relationships for the Java Language Specification
Grammar convergence is a method that helps discovering relationships between
different grammars of the same language or different language versions. The key
element of the method is the operational, transformation-based representation
of those relationships. Given input grammars for convergence, they are
transformed until they are structurally equal. The transformations are composed
from primitive operators; properties of these operators and the composed chains
provide quantitative and qualitative insight into the relationships between the
grammars at hand. We describe a refined method for grammar convergence, and we
use it in a major study, where we recover the relationships between all the
grammars that occur in the different versions of the Java Language
Specification (JLS). The relationships are represented as grammar
transformation chains that capture all accidental or intended differences
between the JLS grammars. This method is mechanized and driven by nominal and
structural differences between pairs of grammars that are subject to
asymmetric, binary convergence steps. We present the underlying operator suite
for grammar transformation in detail, and we illustrate the suite with many
examples of transformations on the JLS grammars. We also describe the
extraction effort, which was needed to make the JLS grammars amenable to
automated processing. We include substantial metadata about the convergence
process for the JLS so that the effort becomes reproducible and transparent
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