4,738 research outputs found
Decidability and Expressiveness of Finitely Representable Recognizable Graph Languages
Recognizable graph languages are a generalization of regular (word) languages to graphs (as well as arbitrary categories). Recently automaton functors were proposed as acceptors of recognizable graph languages. They promise to be a useful tool for the verification of dynamic systems, for example for invariant checking. Since automaton functors may contain an infinite number of finite state sets, one must restrict to finitely representable ones for implementation reasons. In this paper we take into account two such finite representations: primitive recursive automaton functors - in which the automaton functor can be constructed on-the-fly by a primitive recursive function -, and bounded automaton functors - in which the interface size of the graphs (cf. path width) is bounded, so that the automaton functor can be explicitly represented. We show that the language classes of both kinds of automaton functor are closed under boolean operations, and compare the expressiveness of the two paradigms with hyperedge replacement grammars. In addition we show that the emptiness and equivalence problem are decidable for bounded automaton functors, but undecidable for primitive recursive automaton functors
Efficient Implementation of Automaton Functors for the Verification of Graph Transformation Systems
In this paper we show new applications for recognizable graph languages to invariant checking. Furthermore we present details about techniques we used for an implementation of a tool suite for (finite) automaton functors which generalize finite automata to the setting of recognizable (graph) languages. In order to develop an efficient implementation we take advantage of Binary Decision Diagrams (BDDs)
Formal Derivation of Concurrent Garbage Collectors
Concurrent garbage collectors are notoriously difficult to implement
correctly. Previous approaches to the issue of producing correct collectors
have mainly been based on posit-and-prove verification or on the application of
domain-specific templates and transformations. We show how to derive the upper
reaches of a family of concurrent garbage collectors by refinement from a
formal specification, emphasizing the application of domain-independent design
theories and transformations. A key contribution is an extension to the
classical lattice-theoretic fixpoint theorems to account for the dynamics of
concurrent mutation and collection.Comment: 38 pages, 21 figures. The short version of this paper appeared in the
Proceedings of MPC 201
Fuzzy graphs: Algebraic structure and syntactic recognition
© Springer Science+Business Media Dordrecht 2013. Directed fuzzy hypergraphs are introduced as a generalization of both crisp directed hypergraphs and directed fuzzy graphs. It is proved that the set of all directed fuzzy hypergraphs can be structured into a magmoid with operations graph composition and disjoint union. In this framework a notion of syntactic recognition inside magmoids is defined. The corresponding class is proved to be closed under boolean operations and inverse mor-phisms of magmoids. Moreover, the language of all strongly connected fuzzy graphs and the language that consists of all fuzzy graphs that have at least one directed path from the begin node to the end node through edges with membership grade 1 are recognizable. Additionally, a useful characterization of recognizability through left derivatives is also achieved
An automated verfication tool for expert systems
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaf 47).by Alexandra Y. Pau.M.Eng
Recognizable Graph Languages for Checking Invariants
We generalize the order-theoretic variant of the Myhill-Nerode theorem to graph languages, and characterize the recognizable graph languages as the class of languages for which the Myhill-Nerode quasi order is a well quasi order. In the second part of the paper we restrict our attention to graphs of bounded interface size, and use Myhill-Nerode quasi orders to verify that, for such bounded graphs, a recognizable graph property is an invariant of a graph transformation system. A recognizable graph property is a recognizable graph language, given as an automaton functor. Finally, we present an algorithm to approximate the Myhill-Nerode ordering
Deterministic Automata for Unordered Trees
Automata for unordered unranked trees are relevant for defining schemas and
queries for data trees in Json or Xml format. While the existing notions are
well-investigated concerning expressiveness, they all lack a proper notion of
determinism, which makes it difficult to distinguish subclasses of automata for
which problems such as inclusion, equivalence, and minimization can be solved
efficiently. In this paper, we propose and investigate different notions of
"horizontal determinism", starting from automata for unranked trees in which
the horizontal evaluation is performed by finite state automata. We show that a
restriction to confluent horizontal evaluation leads to polynomial-time
emptiness and universality, but still suffers from coNP-completeness of the
emptiness of binary intersections. Finally, efficient algorithms can be
obtained by imposing an order of horizontal evaluation globally for all
automata in the class. Depending on the choice of the order, we obtain
different classes of automata, each of which has the same expressiveness as
CMso.Comment: In Proceedings GandALF 2014, arXiv:1408.556
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