8,125 research outputs found
Pattern matching of compressed terms and contexts and polynomial rewriting
A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be performed in time O(ncjVar(s)j), including the construction of the compressed substitution, and a representation of all occurrences. We show that the special case where s is uncompressed can be performed in polynomial time. As a nice application we show that for an equational deduction of t to t0 by an equality axiom l = r (a rewrite) a single step can be performed in polynomial time in the size of compression of t and l; r if the number of variables is fixed in l. We also show that n rewriting steps can be performed in polynomial time, if the equational axioms are compressed and assumed to be constant for the rewriting sequence. Another potential application are querying mechanisms on compressed XML-data bases
Equational reasoning with context-free families of string diagrams
String diagrams provide an intuitive language for expressing networks of
interacting processes graphically. A discrete representation of string
diagrams, called string graphs, allows for mechanised equational reasoning by
double-pushout rewriting. However, one often wishes to express not just single
equations, but entire families of equations between diagrams of arbitrary size.
To do this we define a class of context-free grammars, called B-ESG grammars,
that are suitable for defining entire families of string graphs, and crucially,
of string graph rewrite rules. We show that the language-membership and
match-enumeration problems are decidable for these grammars, and hence that
there is an algorithm for rewriting string graphs according to B-ESG rewrite
patterns. We also show that it is possible to reason at the level of grammars
by providing a simple method for transforming a grammar by string graph
rewriting, and showing admissibility of the induced B-ESG rewrite pattern.Comment: International Conference on Graph Transformation, ICGT 2015. The
final publication is available at Springer via
http://dx.doi.org/10.1007/978-3-319-21145-9_
Separating Dependency from Constituency in a Tree Rewriting System
In this paper we present a new tree-rewriting formalism called Link-Sharing
Tree Adjoining Grammar (LSTAG) which is a variant of synchronous TAGs. Using
LSTAG we define an approach towards coordination where linguistic dependency is
distinguished from the notion of constituency. Such an approach towards
coordination that explicitly distinguishes dependencies from constituency gives
a better formal understanding of its representation when compared to previous
approaches that use tree-rewriting systems which conflate the two issues.Comment: 7 pages, 6 Postscript figures, uses fullname.st
A rewriting grammar for heat exchanger network structure evolution with stream splitting
The design of cost optimal heat exchanger networks is a difficult optimisation problem due
both to the nonlinear models required and also the combinatorial size of the search space.
When stream splitting is considered, the combinatorial aspects make the problem even harder.
This paper describes the implementation of a two level evolutionary algorithm based on a
string rewriting grammar for the evolution of the heat exchanger network structure. A biological analogue of genotypes and phenotypes is used to describe structures and specific solutions respectively. The top level algorithm evolves structures while the lower level optimises specific
structures. The result is a hybrid optimisation procedure which can identify the best structures including stream splitting. Case studies from the literature are presented to demonstrate the capabilities of the novel procedure
12th International Workshop on Termination (WST 2012) : WST 2012, February 19ā23, 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 19ā23, 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
Combining Insertion and Deletion in RNA-editing Preserves Regularity
Inspired by RNA-editing as occurs in transcriptional processes in the living
cell, we introduce an abstract notion of string adjustment, called guided
rewriting. This formalism allows simultaneously inserting and deleting
elements. We prove that guided rewriting preserves regularity: for every
regular language its closure under guided rewriting is regular too. This
contrasts an earlier abstraction of RNA-editing separating insertion and
deletion for which it was proved that regularity is not preserved. The
particular automaton construction here relies on an auxiliary notion of slice
sequence which enables to sweep from left to right through a completed rewrite
sequence.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347
Linear Compressed Pattern Matching for Polynomial Rewriting (Extended Abstract)
This paper is an extended abstract of an analysis of term rewriting where the
terms in the rewrite rules as well as the term to be rewritten are compressed
by a singleton tree grammar (STG). This form of compression is more general
than node sharing or representing terms as dags since also partial trees
(contexts) can be shared in the compression. In the first part efficient but
complex algorithms for detecting applicability of a rewrite rule under
STG-compression are constructed and analyzed. The second part applies these
results to term rewriting sequences.
The main result for submatching is that finding a redex of a left-linear rule
can be performed in polynomial time under STG-compression.
The main implications for rewriting and (single-position or parallel)
rewriting steps are: (i) under STG-compression, n rewriting steps can be
performed in nondeterministic polynomial time. (ii) under STG-compression and
for left-linear rewrite rules a sequence of n rewriting steps can be performed
in polynomial time, and (iii) for compressed rewrite rules where the left hand
sides are either DAG-compressed or ground and STG-compressed, and an
STG-compressed target term, n rewriting steps can be performed in polynomial
time.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599
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
Complexity Hierarchies and Higher-Order Cons-Free Rewriting
Constructor rewriting systems are said to be cons-free if, roughly,
constructor terms in the right-hand sides of rules are subterms of constructor
terms in the left-hand side; the computational intuition is that rules cannot
build new data structures. It is well-known that cons-free programming
languages can be used to characterize computational complexity classes, and
that cons-free first-order term rewriting can be used to characterize the set
of polynomial-time decidable sets.
We investigate cons-free higher-order term rewriting systems, the complexity
classes they characterize, and how these depend on the order of the types used
in the systems. We prove that, for every k 1, left-linear cons-free
systems with type order k characterize ETIME if arbitrary evaluation is
used (i.e., the system does not have a fixed reduction strategy).
The main difference with prior work in implicit complexity is that (i) our
results hold for non-orthogonal term rewriting systems with possible rule
overlaps with no assumptions about reduction strategy, (ii) results for such
term rewriting systems have previously only been obtained for k = 1, and with
additional syntactic restrictions on top of cons-freeness and left-linearity.
Our results are apparently among the first implicit characterizations of the
hierarchy E = ETIME ETIME .... Our work
confirms prior results that having full non-determinism (via overlaps of rules)
does not directly allow characterization of non-deterministic complexity
classes like NE. We also show that non-determinism makes the classes
characterized highly sensitive to minor syntactic changes such as admitting
product types or non-left-linear rules.Comment: Extended version (with appendices) of a paper published in FSCD 201
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