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Complexity Analysis of Precedence Terminating Infinite Graph Rewrite Systems

Naohi Eguchi
2015 Electronic Proceedings in Theoretical Computer Science  
The general form of safe recursion (or ramified recurrence) can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which  ...  We show that for any precedence terminating infinite graph rewrite system G with a specific argument separation, both the runtime complexity of G and the size of every normal form in G can be polynomially  ...  graph rewrite rules. • This work: Complexity analysis of precedence terminating infinite GRSs based on unfolding graph rewrite rules. • Seems more appropriate to measure runtime complexity by the depth  ... 
doi:10.4204/eptcs.183.3 fatcat:qod7ptvahbhyfieysvnjccto34

Constraint Validation in Model Compilers

László Lengyel, Tihamér Levendovszky, Hassan Charaf
2006 Journal of Object Technology  
Our metamodel-based approach uses graph rewriting techniques for model transformation.  ...  This work presents the Rule Constraint Validator (RCV) algorithm, the Invariant Analysis (IA) algorithm, the Persistent Analysis (PA) algorithm and the combination of the RCV and PA algorithms which results  ...  ACKNOWLEDGEMENTS The activities described in this paper supported, in part, by Information Technology Innovation and Knowledge Centre.  ... 
doi:10.5381/jot.2006.5.4.a3 fatcat:xkm3iawfbraodoxvwvy2tqj3ey

Complexity of Acyclic Term Graph Rewriting

Martin Avanzini, Georg Moser, Marc Herbstritt
2016 International Conference on Rewriting Techniques and Applications  
However, the automated complexity analysis of term graph rewriting has received little to no attention. With this work, we provide first steps towards overcoming this situation.  ...  In contrast to term rewriting, term graph rewriting permits sharing of common sub-expressions, and consequently is able to capture more closely reasonable implementations of rule based languages.  ...  However, the automated complexity analysis of term graph rewriting has received little to no attention. This is somewhat surprising.  ... 
doi:10.4230/lipics.fscd.2016.10 dblp:conf/rta/AvanziniM16 fatcat:fmrro4nvb5dpzkzeozyrfipalq

Derivational Complexity Is an Invariant Cost Model [chapter]

Ugo Dal Lago, Simone Martini
2010 Lecture Notes in Computer Science  
This has some interesting consequences for (asymptotic) complexity analysis, since many existing methodologies only guarantee bounded derivational complexity.  ...  We show that in the context of orthogonal term rewriting systems, derivational complexity is an invariant cost model, both in innermost and in outermost reduction.  ...  Acknowledgments We owe to Guillaume Bonfante the observation that our results, previously formulated for constructor orthogonal rewriting systems, hold indeed for any orthogonal system, as it is now stated  ... 
doi:10.1007/978-3-642-15331-0_7 fatcat:z2ycl4f5gbgundcmao3c47fghq

Complexity, Graphs, and the Dependency Pair Method [chapter]

Nao Hirokawa, Georg Moser
2008 Lecture Notes in Computer Science  
., polynomial runtime complexities of term rewrite systems automatically. We extend our earlier results by revisiting dependency graphs in the context of complexity analysis.  ...  The gain in power is even more signicant when compared to existing methods that directly, i.e., without the use of transformations, induce feasible runtime complexities.  ...  This research is partly supported by FWF (Austrian Science Fund) project P20133, Grant-in-Aid for Young Scientists 20800022 of the Ministry of Education, Culture, Sports, Science and Technology of Japan  ... 
doi:10.1007/978-3-540-89439-1_45 fatcat:ilsskhubgjbqbb6zrdzoerldry

Network Vulnerability Analysis Through Vulnerability Take-Grant Model (VTG) [chapter]

Hamid Reza Shahriari, Reza Sadoddin, Rasool Jalili, Reza Zakeri, Ali Reza Omidian
2005 Lecture Notes in Computer Science  
Our analysis is based on a bounded polynomial algorithm, which generates the closure of the Take-Grant graph regarding vulnerabilities.  ...  We extend the initial Take-Grant model to address the notion of vulnerabilities and introduce the vulnerabilities rewriting rules to specify how the protection state of the system can be changed by exploiting  ...  Reducing the time complexity of the analysis can be considered as well.  ... 
doi:10.1007/11602897_22 fatcat:v6uyxkahebetxj5hbg6t7i3blu

How to uniformly specify program analysis and transformation with graph rewrite systems [chapter]

Uwe Aßmann
1996 Lecture Notes in Computer Science  
For program analysis we use a simple variant of graph rewrite systems (edge addition rewrite systems). For program transformation we apply more complex graph rewrite systems.  ...  We demonstrate this by several examples and measurements.  ...  Secondly, program analysis has to be specified by graph rewrite systems. For this we supply a special variant of graph rewrite systems, edge addition rewrite systems (EARs) .  ... 
doi:10.1007/3-540-61053-7_57 fatcat:bf24ao2lv5ahvfvhopygkpwfei

Page 4349 of Mathematical Reviews Vol. , Issue 96g [page]

1996 Mathematical Reviews  
Augustin) Exponential time analysis of confluent and boundary eNCE graph languages.  ...  Summary: “eNCE (edge label neighborhood controlled) graph grammars belong to the most powerful graph rewriting systems with single-node graphs on the left-hand side of the productions.  ... 

Automated Complexity Analysis Based on the Dependency Pair Method [article]

Nao Hirokawa, Georg Moser
2011 arXiv   pre-print
This article is concerned with automated complexity analysis of term rewrite systems.  ...  Since these systems underlie much of declarative programming, time complexity of functions defined by rewrite systems is of particular interest.  ...  Weak Dependency Graphs In this section we extend the above refinements by revisiting dependency graphs in the context of complexity analysis.  ... 
arXiv:1102.3129v2 fatcat:diqzpia4dzglvmh4f5aakdgllu

egg: Fast and Extensible Equality Saturation [article]

Max Willsey, Chandrakana Nandi, Yisu Remy Wang, Oliver Flatt, Zachary Tatlock, Pavel Panchekha
2020 arXiv   pre-print
Equality saturation workloads exhibit distinct characteristics and often require ad-hoc e-graph extensions to incorporate transformations beyond purely syntactic rewrites.  ...  Although they were originally developed in the late 1970s for use in automated theorem provers, a more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven  ...  This work was supported in part by the Applications Driving Architectures (ADA) Research Center, a JUMP Center co-sponsored by SRC and DARPA, as well as the National Science Foundation under Grant Nos.  ... 
arXiv:2004.03082v3 fatcat:jqqec6vamnaejcl2fqw3tq2nyy

Graph Rewriting Techniques in Engineering Design

Lothar Kolbeck, Simon Vilgertshofer, Jimmy Abualdenien, André Borrmann
2022 Frontiers in Built Environment  
On top of these graph structures, graph rewriting techniques provide another powerful layer of technology.  ...  By enabling the formal definition of rules for transforming graph structures, they allow on the one hand side to formally capture the engineering development process.  ...  For engineering design, the use of graph rewriting methods can enable the automation of complex design sequences.  ... 
doi:10.3389/fbuil.2021.815153 fatcat:my2r2ov4izey5hkmqiohpcluau

Proving Termination of Programs Automatically with AProVE [chapter]

Jürgen Giesl, Marc Brockschmidt, Fabian Emmes, Florian Frohn, Carsten Fuhs, Carsten Otto, Martin Plücker, Peter Schneider-Kamp, Thomas Ströder, Stephanie Swiderski, René Thiemann
2014 Lecture Notes in Computer Science  
AProVE is a system for automatic termination and complexity proofs of Java, C, Haskell, Prolog, and term rewrite systems (TRSs).  ...  Then, a wide range of techniques is employed to prove termination and to infer complexity bounds for the resulting TRSs.  ...  Non-termination of TRSs is detected by suitable adaptions of narrowing [15] . For complexity analysis, AProVE infers runtime complexity of innermost rewriting.  ... 
doi:10.1007/978-3-319-08587-6_13 fatcat:7wpvmvkp6jhhxey7ornjsfwfgm

Cumulative subject index

1990 Information and Computation  
89 A Aanderaa argument clean version and new extensions, 88, 88 Agreement Byzantine, related environment, knowledge and common knowledge in: crash failures, 88, 156 Algebras and first-order logic for complexity  ...  Arimoto-Blahut, in calculating capacity of continuous-input discrete-output memoryless channels, 86, 1 Berlekamp-Massey, extension to n dimensions, 84, 207 for deciding confluence of finite ground term rewrite  ...  , 196 regular, nondeterminism in, measurement, 86, 179 Permanent and determinant. problem. in arithmetic complexity, 84, 119 Semantics possible-world, in analysis of specification logic, 85, 135 Petri  ... 
doi:10.1016/0890-5401(90)90012-7 fatcat:abh2kjcxfveulfizk3aa5ifc64

Rule Invariants in Graph Transformation Systems for Analyzing Safety-Critical Systems [chapter]

Julia Padberg, Bettina E. Enders
2002 Lecture Notes in Computer Science  
The focus of this paper lies in the analysis of graph transformation systems by analysis techniques transferred from Petri nets.  ...  This allows a suitable analysis of graph transformation systems as is exemplified by a safety-critical system specification in the area of human-computer interaction.  ...  We express the crucial notions for invariant analysis in terms of graphs, graph rewrite rules and transformations.  ... 
doi:10.1007/3-540-45832-8_25 fatcat:7lijr2kjnzarbnqzc5vexuq7zm

Symbolic evaluation graphs and term rewriting

Jürgen Giesl, Thomas Ströder, Peter Schneider-Kamp, Fabian Emmes, Carsten Fuhs
2012 Proceedings of the 14th symposium on Principles and practice of declarative programming - PPDP '12  
There exist many powerful techniques to analyze termination and complexity of term rewrite systems (TRSs). Our goal is to use these techniques for the analysis of other programming languages as well.  ...  In particular, one can generate TRSs from such graphs and apply existing tools for termination or complexity analysis of TRSs to infer information on the termination or complexity of the original logic  ...  Conclusion We presented the symbolic evaluation graph and the use of term rewriting as a general methodology for the analysis of logic programs.  ... 
doi:10.1145/2370776.2370778 dblp:conf/ppdp/GieslSSEF12 fatcat:4mtadf3mjzb53gnsn6t7bnsrri
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