Model Checking

The Temporal Logic of Reactive and Concurrent Systems: Specification

Ordered Binary-Decision Diagrams (OBDDs) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satisfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as graph algorithms on OBDD data structures. Using OBDDs, a wide variety of problems can be solved through symbolic analysis. First, the possible variations in system parameters and operating conditions are encoded with Boolean variables. Then the system is evaluated for all variations by a sequence of OBDD operations. Researchers have thus solved a number of problems in digital-system design, finite-state system analysis, artificial intelligence, and mathematical logic. This paper describes the OBDD data structure and surveys a number of applications that have been solved by OBDD-based symbolic analysis.

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Symbolic Boolean manipulation with ordered binary-decision diagrams

1: Magnetic Particles: Preparation, Properties and Applications: M. Ozaki. 2: Maghemite (gamma-Fe2O3): A Versatile Magnetic Colloidal Material C.J. Serna, M.P. Morales. 3: Dynamics of Adsorption and Oxidation of Organic Molecules on Illuminated Titanium Dioxide Particles Immersed in Water M.A. Blesa, R.J. Candal, S.A. Bilmes. 4: Colloidal Aggregation in Two-Dimensions A. Moncho-Jorda, F. Martinez-Lopez, M.A. Cabrerizo-Vilchez, R. Hidalgo Alvarez, M. Quesada-PMerez. 5: Kinetics of Particle and Protein Adsorption Z. Adamczyk.

Surface and Colloid Science

ing WS1S Systems to Verify Parameterized Networks . . . . . . . . . . . . 188 Kai Baukus, Saddek Bensalem, Yassine Lakhnech and Karsten Stahl FMona: A Tool for Expressing Validation Techniques over Infinite State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 J.-P. Bodeveix and M. Filali Transitive Closures of Regular Relations for Verifying Infinite-State Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Bengt Jonsson and Marcus Nilsson Diagnostic and Test Generation Using Static Analysis to Improve Automatic Test Generation . . . . . . . . . . . . . 235 Marius Bozga, Jean-Claude Fernandez and Lucian Ghirvu Efficient Diagnostic Generation for Boolean Equation Systems . . . . . . . . . . . . 251 Radu Mateescu Efficient Model-Checking Compositional State Space Generation with Partial Order Reductions for Asynchronous Communicating Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Jean-Pierre Krimm and Laurent Mounier Checking for CFFD-Preorder with Tester Processes . . . . . . . . . . . . . . . . . . . . . . . 283 Juhana Helovuo and Antti Valmari Fair Bisimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Thomas A. Henzinger and Sriram K. Rajamani Integrating Low Level Symmetries into Reachability Analysis . . . . . . . . . . . . . 315 Karsten Schmidt Model-Checking Tools Model Checking Support for the ASM High-Level Language . . . . . . . . . . . . . . 331 Giuseppe Del Castillo and Kirsten Winter Table of

Tools and Algorithms for the Construction and Analysis of Systems. Proc. TACAS 2009

In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the BDD representation is often smaller than any other conventional special-case representation: for the n×n Walsh matrix, for example, the BDD representation is of size O(log n). No other special-case representation in common use represents this matrix in space less than O(n²). We describe termwise, row, column, block, and diagonal selection over these matrices, standard an Strassen matrix multiplication, and LU factorization. We demonstrate that the complexity of each of these operations over the BDD representation is no greater than that over any standard representation. Further, we demonstrate that complete pivoting is no more difficult over these matrices than partial pivoting. Finally, we consider an example, the Walsh Spectrum of a Boolean function.

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Multi-Terminal Binary Decision Diagrams: An Efficient DataStructure for Matrix Representation

The Walsh transform has numerous applications in computer-aided design, but the usefulness of these techniques in practice has been limited by the size of the boolean functions that can be transformed. Currently available techniques limit the functions to less than 20 variables. In this paper, we show how to compute concise representations of the Walsh transform for functions with several hundred variables. We have applied our techniques to boolean technology mapping and, in certain cases, we obtained a speed up of as much as 50% for the matching phase.

Spectral Transforms for Large Boolean Functions withApplications to Technology Mapping

Hardware description languages (HDLs) are used today to describe circuits at all levels. In large HDL programs, there is a need for source code reduction techniques to address a myriad of problems in formal verification, design, simulation, and testing. Program slicing is a static program analysis technique that allows an analyst to automatically extract portions of programs relevant to the aspects being analyzed. We extend program slicing to HDLs, thus allowing for automatic program reduction to allow the user to focus on relevant code portions. We have implemented a VHDL slicing tool composed of a general inter-procedural slicer and a front-end that captures VHDL execution semantics. This paper provides an overview of program slicing, a discussion of how to slice VHDL programs, a description of the resulting tool, and a brief overview of some applications and experimental results.

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Program Slicing of Hardware Description Languages

Design verification poses a very practical problem during circuit synthesis. Learning based verification techniques prove to be an attractive option for verifying two circuits with internal gates having simple functional relationships. We present a verification method which employs a learning technique based on symbolic manipulation and which can more efficiently learn indirect implications. The method can also learn some useful functional implications. We also present a framework in which an indirect implication technique is integrated with an OBDD based verification tool. We present highly efficient verification results on some ISCAS circuits as well as on some very hard industrial circuits.

Advanced Verification Techniques Based on Learning

Ordered binary decision diagrams (OBDDs) use restricted decision trees with shared subgraphs. The ordering of variables is fixed throughout an OBDD diagram. However, the size of an OBDD is very sensitive to variable ordering, especially for large circuits. The results of experiments in variable ordering using an experimentally practical algorithm are presented. The algorithm is basically a depth-first traversal through a circuit from the output to the inputs. With this algorithm, circuits having more than 3000 gates and more than 100 inputs can be expressed in reasonable CPU time and with practical memory requirements. >

Masahiro Fujita

Papers

Multi-Terminal Binary Decision Diagrams: An Efficient DataStructure for Matrix Representation

Spectral Transforms for Large Boolean Functions withApplications to Technology Mapping

Program Slicing of Hardware Description Languages

Advanced Verification Techniques Based on Learning

Variable ordering algorithms for ordered binary decision diagrams and their evaluation