22,126 research outputs found
12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser
This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto
Non-simplifying Graph Rewriting Termination
So far, a very large amount of work in Natural Language Processing (NLP) rely
on trees as the core mathematical structure to represent linguistic
informations (e.g. in Chomsky's work). However, some linguistic phenomena do
not cope properly with trees. In a former paper, we showed the benefit of
encoding linguistic structures by graphs and of using graph rewriting rules to
compute on those structures. Justified by some linguistic considerations, graph
rewriting is characterized by two features: first, there is no node creation
along computations and second, there are non-local edge modifications. Under
these hypotheses, we show that uniform termination is undecidable and that
non-uniform termination is decidable. We describe two termination techniques
based on weights and we give complexity bound on the derivation length for
these rewriting system.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599
Extensional and Intensional Strategies
This paper is a contribution to the theoretical foundations of strategies. We
first present a general definition of abstract strategies which is extensional
in the sense that a strategy is defined explicitly as a set of derivations of
an abstract reduction system. We then move to a more intensional definition
supporting the abstract view but more operational in the sense that it
describes a means for determining such a set. We characterize the class of
extensional strategies that can be defined intensionally. We also give some
hints towards a logical characterization of intensional strategies and propose
a few challenging perspectives
Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings
We introduce techniques for proving uniform termination of graph
transformation systems, based on matrix interpretations for string rewriting.
We generalize this technique by adapting it to graph rewriting instead of
string rewriting and by generalizing to ordered semirings. In this way we
obtain a framework which includes the tropical and arctic type graphs
introduced in a previous paper and a new variant of arithmetic type graphs.
These type graphs can be used to assign weights to graphs and to show that
these weights decrease in every rewriting step in order to prove termination.
We present an example involving counters and discuss the implementation in the
tool Grez
Deriving Bisimulation Congruences using 2-Categories
We introduce G-relative-pushouts (GRPO) which are a 2-categorical generalisation of relative-pushouts (RPO). They are suitable for deriving labelled transition systems (LTS) for process calculi where terms are viewed modulo structural congruence. We develop their basic properties and show that bisimulation on the LTS derived via GRPOs is a congruence, provided that sufficiently many GRPOs exist. The theory is applied to a simple subset of CCS and the resulting LTS is compared to one derived using a procedure proposed by Sewell
On Quasi-Interpretations, Blind Abstractions and Implicit Complexity
Quasi-interpretations are a technique to guarantee complexity bounds on
first-order functional programs: with termination orderings they give in
particular a sufficient condition for a program to be executable in polynomial
time, called here the P-criterion. We study properties of the programs
satisfying the P-criterion, in order to better understand its intensional
expressive power. Given a program on binary lists, its blind abstraction is the
nondeterministic program obtained by replacing lists by their lengths (natural
numbers). A program is blindly polynomial if its blind abstraction terminates
in polynomial time. We show that all programs satisfying a variant of the
P-criterion are in fact blindly polynomial. Then we give two extensions of the
P-criterion: one by relaxing the termination ordering condition, and the other
one (the bounded value property) giving a necessary and sufficient condition
for a program to be polynomial time executable, with memoisation.Comment: 18 page
Rewriting Abstract Structures: Materialization Explained Categorically
The paper develops an abstract (over-approximating) semantics for
double-pushout rewriting of graphs and graph-like objects. The focus is on the
so-called materialization of left-hand sides from abstract graphs, a central
concept in previous work. The first contribution is an accessible, general
explanation of how materializations arise from universal properties and
categorical constructions, in particular partial map classifiers, in a topos.
Second, we introduce an extension by enriching objects with annotations and
give a precise characterization of strongest post-conditions, which are
effectively computable under certain assumptions
Deriving Bisimulation Congruences: A 2-Categorical Approach
We introduce G-relative-pushouts (GRPO) which are a 2-categorical generalisation of relative-pushouts (RPO). They are suitable for deriving labelled transition systems (LTS) for process calculi where terms are viewed modulo structural congruence. We develop their basic properties and show that bisimulation on the LTS derived via GRPOs is a congruence, provided that sufficiently many GRPOs exist. The theory is applied to a simple subset of CCS and the resulting LTS is compared to one derived using a procedure proposed by Sewell
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