1,439 research outputs found
On the logical definability of certain graph and poset languages
We show that it is equivalent, for certain sets of finite graphs, to be
definable in CMS (counting monadic second-order logic, a natural extension of
monadic second-order logic), and to be recognizable in an algebraic framework
induced by the notion of modular decomposition of a finite graph. More
precisely, we consider the set of composition operations on graphs
which occur in the modular decomposition of finite graphs. If is a subset
of , we say that a graph is an \calF-graph if it can be
decomposed using only operations in . A set of -graphs is recognizable if
it is a union of classes in a finite-index equivalence relation which is
preserved by the operations in . We show that if is finite and its
elements enjoy only a limited amount of commutativity -- a property which we
call weak rigidity, then recognizability is equivalent to CMS-definability.
This requirement is weak enough to be satisfied whenever all -graphs are
posets, that is, transitive dags. In particular, our result generalizes Kuske's
recent result on series-parallel poset languages
A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency
This research started with an algebra for reasoning about rely/guarantee
concurrency for a shared memory model. The approach taken led to a more
abstract algebra of atomic steps, in which atomic steps synchronise (rather
than interleave) when composed in parallel. The algebra of rely/guarantee
concurrency then becomes an instantiation of the more abstract algebra. Many of
the core properties needed for rely/guarantee reasoning can be shown to hold in
the abstract algebra where their proofs are simpler and hence allow a higher
degree of automation. The algebra has been encoded in Isabelle/HOL to provide a
basis for tool support for program verification.
In rely/guarantee concurrency, programs are specified to guarantee certain
behaviours until assumptions about the behaviour of their environment are
violated. When assumptions are violated, program behaviour is unconstrained
(aborting), and guarantees need no longer hold. To support these guarantees a
second synchronous operator, weak conjunction, was introduced: both processes
in a weak conjunction must agree to take each atomic step, unless one aborts in
which case the whole aborts. In developing the laws for parallel and weak
conjunction we found many properties were shared by the operators and that the
proofs of many laws were essentially the same. This insight led to the idea of
generalising synchronisation to an abstract operator with only the axioms that
are shared by the parallel and weak conjunction operator, so that those two
operators can be viewed as instantiations of the abstract synchronisation
operator. The main differences between parallel and weak conjunction are how
they combine individual atomic steps; that is left open in the axioms for the
abstract operator.Comment: Extended version of a Formal Methods 2016 paper, "An algebra of
synchronous atomic steps
A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency
This research started with an algebra for reasoning about rely/guarantee
concurrency for a shared memory model. The approach taken led to a more
abstract algebra of atomic steps, in which atomic steps synchronise (rather
than interleave) when composed in parallel. The algebra of rely/guarantee
concurrency then becomes an instantiation of the more abstract algebra. Many of
the core properties needed for rely/guarantee reasoning can be shown to hold in
the abstract algebra where their proofs are simpler and hence allow a higher
degree of automation. The algebra has been encoded in Isabelle/HOL to provide a
basis for tool support for program verification.
In rely/guarantee concurrency, programs are specified to guarantee certain
behaviours until assumptions about the behaviour of their environment are
violated. When assumptions are violated, program behaviour is unconstrained
(aborting), and guarantees need no longer hold. To support these guarantees a
second synchronous operator, weak conjunction, was introduced: both processes
in a weak conjunction must agree to take each atomic step, unless one aborts in
which case the whole aborts. In developing the laws for parallel and weak
conjunction we found many properties were shared by the operators and that the
proofs of many laws were essentially the same. This insight led to the idea of
generalising synchronisation to an abstract operator with only the axioms that
are shared by the parallel and weak conjunction operator, so that those two
operators can be viewed as instantiations of the abstract synchronisation
operator. The main differences between parallel and weak conjunction are how
they combine individual atomic steps; that is left open in the axioms for the
abstract operator.Comment: Extended version of a Formal Methods 2016 paper, "An algebra of
synchronous atomic steps
A transformation-driven approach to automate feedback verification results
International audienceThe integration of formal verification methods in modeling activities is a key issue to ensure the correctness of complex system design models. In this purpose, the most common approach consists in defining a translational semantics mapping the abstract syntax of the designer dedicated Domain-Specific Modeling Language (DSML) to a formal verification dedicated semantic domain in order to reuse the available powerful verification technologies. Formal verification is thus usually achieved using model transformations. However, the verification results are available in the formal domain which significantly impairs their use by the system designer which is usually not an expert of the formal technologies. In this paper, we introduce a novel approach based on Higher-Order transformations that analyze and instrument the transformation that expresses the semantics in order to produce traceability data to automatize the back propagation of verification results to the DSML end-user
The Lambek calculus with iteration: two variants
Formulae of the Lambek calculus are constructed using three binary
connectives, multiplication and two divisions. We extend it using a unary
connective, positive Kleene iteration. For this new operation, following its
natural interpretation, we present two lines of calculi. The first one is a
fragment of infinitary action logic and includes an omega-rule for introducing
iteration to the antecedent. We also consider a version with infinite (but
finitely branching) derivations and prove equivalence of these two versions. In
Kleene algebras, this line of calculi corresponds to the *-continuous case. For
the second line, we restrict our infinite derivations to cyclic (regular) ones.
We show that this system is equivalent to a variant of action logic that
corresponds to general residuated Kleene algebras, not necessarily
*-continuous. Finally, we show that, in contrast with the case without division
operations (considered by Kozen), the first system is strictly stronger than
the second one. To prove this, we use a complexity argument. Namely, we show,
using methods of Buszkowski and Palka, that the first system is -hard,
and therefore is not recursively enumerable and cannot be described by a
calculus with finite derivations
Inductive Definition and Domain Theoretic Properties of Fully Abstract
A construction of fully abstract typed models for PCF and PCF^+ (i.e., PCF +
"parallel conditional function"), respectively, is presented. It is based on
general notions of sequential computational strategies and wittingly consistent
non-deterministic strategies introduced by the author in the seventies.
Although these notions of strategies are old, the definition of the fully
abstract models is new, in that it is given level-by-level in the finite type
hierarchy. To prove full abstraction and non-dcpo domain theoretic properties
of these models, a theory of computational strategies is developed. This is
also an alternative and, in a sense, an analogue to the later game strategy
semantics approaches of Abramsky, Jagadeesan, and Malacaria; Hyland and Ong;
and Nickau. In both cases of PCF and PCF^+ there are definable universal
(surjective) functionals from numerical functions to any given type,
respectively, which also makes each of these models unique up to isomorphism.
Although such models are non-omega-complete and therefore not continuous in the
traditional terminology, they are also proved to be sequentially complete (a
weakened form of omega-completeness), "naturally" continuous (with respect to
existing directed "pointwise", or "natural" lubs) and also "naturally"
omega-algebraic and "naturally" bounded complete -- appropriate generalisation
of the ordinary notions of domain theory to the case of non-dcpos.Comment: 50 page
Web 2.0, language resources and standards to automatically build a multilingual named entity lexicon
This paper proposes to advance in the current state-of-the-art of automatic Language Resource (LR) building by taking into consideration three elements: (i) the knowledge available in existing LRs, (ii) the vast amount of information available from the collaborative paradigm that has emerged from the Web 2.0 and (iii) the use of standards to improve interoperability. We present a case study in which a set of LRs for different languages (WordNet for English and Spanish and Parole-Simple-Clips for Italian) are
extended with Named Entities (NE) by exploiting Wikipedia and the aforementioned LRs. The practical result is a multilingual NE lexicon connected to these LRs and to two ontologies: SUMO and SIMPLE. Furthermore, the paper addresses an important problem which affects the Computational Linguistics area in the present, interoperability, by making use of the ISO LMF standard to encode this lexicon. The different steps of the procedure (mapping, disambiguation, extraction, NE identification and postprocessing) are comprehensively explained and evaluated. The resulting resource contains 974,567, 137,583 and 125,806 NEs for English, Spanish and Italian respectively. Finally, in order to check the usefulness of the constructed resource, we apply it into a state-of-the-art Question Answering system and evaluate its impact; the NE lexicon improves the system’s accuracy by 28.1%. Compared to previous approaches to build NE repositories, the current proposal represents a step forward in terms of automation, language independence, amount of NEs acquired and richness of the information represented
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