551 research outputs found
An interactive semantics of logic programming
We apply to logic programming some recently emerging ideas from the field of
reduction-based communicating systems, with the aim of giving evidence of the
hidden interactions and the coordination mechanisms that rule the operational
machinery of such a programming paradigm. The semantic framework we have chosen
for presenting our results is tile logic, which has the advantage of allowing a
uniform treatment of goals and observations and of applying abstract
categorical tools for proving the results. As main contributions, we mention
the finitary presentation of abstract unification, and a concurrent and
coordinated abstract semantics consistent with the most common semantics of
logic programming. Moreover, the compositionality of the tile semantics is
guaranteed by standard results, as it reduces to check that the tile systems
associated to logic programs enjoy the tile decomposition property. An
extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory
and Practice of Logic Programmin
On the essence of parallel independence for the double-pushout and sesqui-pushout approaches
Parallel independence between transformation steps is a basic notion in the algebraic approaches to graph transformation, which is at the core of some static analysis techniques like Critical Pair Analysis. We propose a new categorical condition of parallel independence and show its equivalence with two other conditions proposed in the literature, for both left-linear and non-left-linear rules. Next we present some preliminary experimental results aimed at comparing the three conditions with respect to computational efficiency. To this aim, we implemented the three conditions, for left-linear rules only, in the Verigraph system, and used them to check parallel independence of pairs of overlapping redexes generated from some sample graph transformation systems over categories of typed graphs
A Unifying Theory for Graph Transformation
The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO
On the definition of parallel independence in the algebraic approaches to graph transformation
Parallel independence between transformation steps is a basic and well-understood notion of the algebraic approaches to graph transformation, and typically guarantees that the two steps can be applied in any order obtaining the same resulting graph, up to isomorphism. The concept has been redefined for several algebraic approaches as variations of a classical “algebraic” condition, requiring that each matching morphism factorizes through the context graphs of the other transformation step. However, looking at some classical papers on the double-pushout approach, one finds that the original definition of parallel independence was formulated in set-theoretical terms, requiring that the intersection of the images of the two left-hand sides in the host graph is contained in the intersection of the two interface graphs. The relationship between this definition and the standard algebraic one is discussed in this position paper, both in the case of left-linear and non-left-linear rules
Parallelism in AGREE transformations
The AGREE approach to graph transformation allows to specify rules that clone items of the host graph, controlling in a finegrained way how to deal with the edges that are incident, but not matched, to the rewritten part of the graph. Here, we investigate in which ways cloning (with controlled embedding) may affect the dependencies between two rules applied to the same graph. We extend to AGREE the classical notion of parallel independence between the matches of two rules to the same graph, identifying sufficient conditions that guarantee that two rules can be applied in any order leading to the same result
Redundancy and subsumption in high-level replacement systems
System verification in the broadest sense deals with those semantic
properties that can be decided or deduced by analyzing a syntactical
description of the system. Hence, one may consider the notions of
redundancy and subsumption in this context as they are known from the
area of rule-based systems. A rule is redundant if it can be removed
without affecting the semantics of the system; it is subsumed by
another rule if each application of the former one can be replaced by
an application of the latter one with the same effect. In this paper,
redundancy and subsumption are carried over from rule-based systems to
high-level replacement systems, which in turn generalize graph and
hypergraph grammars. The main results presented in this paper are a
characterization of subsumption and a sufficient condition for
redundancy, which involves composite productions.Postprint (published version
Improved Conflict Detection for Graph Transformation with Attributes
In graph transformation, a conflict describes a situation where two
alternative transformations cannot be arbitrarily serialized. When enriching
graphs with attributes, existing conflict detection techniques typically report
a conflict whenever at least one of two transformations manipulates a shared
attribute. In this paper, we propose an improved, less conservative condition
for static conflict detection of graph transformation with attributes by
explicitly taking the semantics of the attribute operations into account. The
proposed technique is based on symbolic graphs, which extend the traditional
notion of graphs by logic formulas used for attribute handling. The approach is
proven complete, i.e., any potential conflict is guaranteed to be detected.Comment: In Proceedings GaM 2015, arXiv:1504.0244
A PBPO+ Graph Rewriting Tutorial
We provide a tutorial introduction to the algebraic graph rewriting formalism
PBPO+. We show how PBPO+ can be obtained by composing a few simple building
blocks, and model the reduction rules for binary decision diagrams as an
example. Along the way, we comment on how alternative design decisions lead to
related formalisms in the literature, such as DPO. We close with a detailed
comparison with Bauderon's double pullback approach.Comment: In Proceedings TERMGRAPH 2022, arXiv:2303.1421
M-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church–Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of M-adhesive categories, where M-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules
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