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Correctness of high-level transformation systems relative to nested conditions

  • ANNEGRET HABEL (a1) and KARL-HEINZ PENNEMANN (a1)
Abstract

In this paper we introduce the notions of nested constraints and application conditions, short nested conditions. For a category associated with a graphical representation such as graphs, conditions are a graphical and intuitive, yet precise, formalism that is well suited to describing structural properties. We show that nested graph conditions are expressively equivalent to first-order graph formulas. A part of the proof includes transformations between two satisfiability notions of conditions, namely -satisfiability and -satisfiability. We consider a number of transformations on conditions that can be composed to construct constraint-guaranteeing and constraint-preserving application conditions, weakest preconditions and strongest postconditions. The restriction of rule applications by conditions can be used to correct transformation systems by pruning transitions leading to states violating given constraints. Weakest preconditions and strongest postconditions can be used to verify the correctness of transformation systems with respect to pre- and postconditions.

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A. Corradini , U. Montanari , F. Rossi , H. Ehrig , R. Heckel and M. Löwe (1997) Algebraic approaches to graph transformation. Part I: Basic concepts and double pushout approach. In: Handbook of Graph Grammars and Computing by Graph Transformation, volume 1, World Scientific163245.

B. Courcelle (1997) The expression of graph properties and graph transformations in monadic second-order logic. In: Handbook of Graph Grammars and Computing by Graph Transformation, volume 1, World Scientific313400.

H. Ehrig (1979) Introduction to the algebraic theory of graph grammars. In: Graph-Grammars and Their Application to Computer Science and Biology. Springer-Verlag Lecture Notes in Computer Science 73 169.

H. Ehrig and A. Habel (1986) Graph grammars with application conditions. In: G. Rozenberg and A. Salomaa (eds.) The Book of L, Springer-Verlag87100.

H. Ehrig , R. Heckel , M. Korff , M. Löwe , L. Ribeiro , A. Wagner and A. Corradini (1997) Algebraic approaches to graph transformation. Part II: Single-pushout approach and comparison with double pushout approach. In: Handbook of Graph Grammars and Computing by Graph Transformation, volume 1, World Scientific247312.

A. Habel and K.-H. Pennemann (2005) Nested constraints and application conditions for high-level structures. In: Formal Methods in Software and System Modeling. Springer-Verlag Lecture Notes in Computer Science 3393 293308.

A. Habel and K.-H. Pennemann (2006) Satisfiability of high-level conditions. In: Graph Transformations (ICGT 2006). Springer-Verlag Lecture Notes in Computer Science 4178 430444.

A. Habel , K.-H. Pennemann and A. Rensink (2006) Weakest preconditions for high-level programs. In: Graph Transformations (ICGT 2006). Springer-Verlag Lecture Notes in Computer Science 4178 445460.

R. Heckel and A. Wagner (1995) Ensuring consistency of conditional graph grammars – a constructive approach. In: Proc. Workshop on Graph Rewriting and Computation (SEGRAGRA'95). Electronic Notes in Theoretical Computer Science 2 95104.

M. Koch , L. V. Mancini and F. Parisi-Presicce (2005) Graph-based specification of access control policies. Journal of Computer and System Sciences 71 133.

M. Koch and F. Parisi-Presicce (2002) Describing policies with graph constraints and rules. In: Graph Transformation (ICGT 2002). Springer-Verlag Lecture Notes in Computer Science 2505 223238.

S. Lack and P. Sobociński (2004) Adhesive categories. In: Proc. of Foundations of Software Science and Computation Structures (FOSSACS'04). Springer-Verlag Lecture Notes in Computer Science 2987 273288.

M. Löwe (1993) Algebraic approach to single-pushout graph transformation. Theoretical Computer Science 109 181224.

F. Orejas , H. Ehrig and U. Prange (2008) A logic of graph constraints. In: Proc. Fundamental Approaches to Software Engineering (FASE'08). Springer-Verlag Lecture Notes in Computer Science 4961 179–19.

K.-H. Pennemann (2008a) An algorithm for approximating the satisfiability problem of high-level conditions. In: Proc. Graph Transformation for Verification and Concurrency (GT-VC'07). Electronic Notes in Theoretical Computer Science 213 7594.

D. Plump and S. Steinert (2004) Towards graph programs for graph algorithms. In: Graph Transformations (ICGT'04). Springer-Verlag Lecture Notes in Computer Science 3256 128143.

A. Rensink (2004) Representing first-order logic by graphs. In: Graph Transformations (ICGT'04). Springer-Verlag Lecture Notes in Computer Science 3256 319335.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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