Results 1  10
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110
Model checking large software specifications
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 1998
"... In this paper, we present our experiences in using symbolic model checking to analyze a specification of a software system for aircraft collision avoidance. Symbolic model checking has been highly successful when applied to hardware systems. We are interested in whether model checking can be effect ..."
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Cited by 137 (6 self)
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In this paper, we present our experiences in using symbolic model checking to analyze a specification of a software system for aircraft collision avoidance. Symbolic model checking has been highly successful when applied to hardware systems. We are interested in whether model checking can be effectively applied to large software specifications. To investigate this, we translated a portion of the statebased system requirements specification of Traffic Alert and Collision Avoidance System II (TCAS II) into input to a symbolic model checker (SMV). We successfully used the symbolic model checker to analyze a number of properties of the system. We report on our experiences, describing our approach to translating the specification to the SMV language, explaining our methods for achieving acceptable performance, and giving a summary of the properties analyzed. Based on our experiences, we discuss the possibility of using model checking to aid specification development by iteratively applying the technique early in the development cycle. We consider the paper to be a data point for optimism about the potential for more widespread application of model checking to software systems.
Verification of Arithmetic Circuits with Binary Moment Diagrams
 IN PROCEEDINGS OF THE 32ND ACM/IEEE DESIGN AUTOMATION CONFERENCE
, 1995
"... Binary Moment Diagrams (BMDs) provide a canonical representations for linear functions similar to the way Binary Decision Diagrams (BDDs) represent Boolean functions. Within the class of linear functions, we can embed arbitrary functions from Boolean variables to integer values. BMDs can thus model ..."
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Cited by 108 (10 self)
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Binary Moment Diagrams (BMDs) provide a canonical representations for linear functions similar to the way Binary Decision Diagrams (BDDs) represent Boolean functions. Within the class of linear functions, we can embed arbitrary functions from Boolean variables to integer values. BMDs can thus model the functionality of data path circuits operating over wordlevel data. Many important functions, including integer multiplication, that cannot be represented efficiently at the bit level with BDDs have simple representations at the word level with BMDs. Furthermore, BMDs can represent Boolean functions with around the same complexity as BDDs. We propose a hierarchical approach to verifying arithmetic circuits, wherecomponentmodulesare first shownto implement their wordlevel specifications. The overall circuit functionality is then verified by composing the component functions and comparing the result to the wordlevel circuit specification. Multipliers with word sizes of up to 256 bits hav...
Markovian Analysis of Large Finite State Machines
 IEEE Transactions on CAD
, 1996
"... Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. In this paper we present symbolic algorithms to compute the steadystate probabilities for very large finite state machines (up to 10 ..."
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Cited by 76 (7 self)
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Regarding finite state machines as Markov chains facilitates the application of probabilistic methods to very large logic synthesis and formal verification problems. In this paper we present symbolic algorithms to compute the steadystate probabilities for very large finite state machines (up to 10 27 states). These algorithms, based on Algebraic Decision Diagrams (ADDs)  an extension of BDDs that allows arbitrary values to be associated with the terminal nodes of the diagrams  determine the steadystate probabilities by regarding finite state machines as homogeneous, discreteparameter Markov chains with finite state spaces, and by solving the corresponding ChapmanKolmogorov equations. We first consider finite state machines with state graphs composed of a single terminal strongly connected component; for this type of systems we have implemented two solution techniques: One is based on the GaussJacobi iteration, the other one is based on simple matrix multiplication. Then we...
ACL2 Theorems about Commercial Microprocessors
, 1996
"... ACL2 is a mechanized mathematical logic intended for use in specifying and proving properties of computing machines. In two independent projects, industrial engineers have collaborated with researchers at Computational Logic, Inc. (CLI), to use ACL2 to model and prove properties of stateoftheart ..."
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Cited by 71 (16 self)
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ACL2 is a mechanized mathematical logic intended for use in specifying and proving properties of computing machines. In two independent projects, industrial engineers have collaborated with researchers at Computational Logic, Inc. (CLI), to use ACL2 to model and prove properties of stateoftheart commercial microprocessors prior to fabrication. In the first project, Motorola, Inc., and CLI collaborated to specify Motorola's complex arithmetic processor (CAP), a singlechip, digital signal processor (DSP) optimized for communications signal processing. Using the specification, we proved the correctness of several CAP microcode programs. The second industrial collaboration involving ACL2 was between Advanced Micro Devices, Inc. (AMD) and CLI. In this work we proved the correctness of the kernel of the floatingpoint division operation on AMD's first Pentiumclass microprocessor, the AMD5K 86. In this paper, we discuss ACL2 and these industrial applications, with particular attention ...
Hybrid decision diagrams  overcoming the limitations of MTBDDs and BMDs
 In Int'l Conf. on CAD
, 1995
"... e�mail � emc�cs.cmu.edu e�mail � masahiro�eecs.berkeley.edu e�mail � xzhao�cs.cmu.edu Abstract � Functions that map boolean vectors into the in� tegers are important for the design and veri�cation of arith� metic circuits. MTBDDs and BMDs have been proposed for representing this class of functions. ..."
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Cited by 58 (3 self)
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e�mail � emc�cs.cmu.edu e�mail � masahiro�eecs.berkeley.edu e�mail � xzhao�cs.cmu.edu Abstract � Functions that map boolean vectors into the in� tegers are important for the design and veri�cation of arith� metic circuits. MTBDDs and BMDs have been proposed for representing this class of functions. We discuss the relation� ship between these methods and describe a generalization called hybrid decision diagrams which is often much more concise. We show how to implement arithemetic operations e�ciently for hybrid decision diagrams. In practice � this is one of the main limitations of BMDs since performing arith� metic operations on functions expressed in this notation can be very expensive. In order to extend symbolic model check� ing algorithms to handle arithmetic properties � it is essential to be able to compute the BDD for the set of variable as� signments that satisfy an arithmetic relation. In our paper� we give an e�cient algorithm for this purpose. Moreover� we prove that for the class of linear expressions � the time complexity of our algorithm is linear in the number of vari� ables. 1
Boolean Expression Diagrams
, 1997
"... This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable proper ..."
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Cited by 54 (5 self)
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This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One is a generalized version of the BDD applyoperator while the other can exploit the structural information of the Boolean expression. This ability is demonstrated by verifying that two di erent circuit implementations of a 16bit multiplier implement the same Boolean function. Using BEDs, this veri cation problem is solved in less than a second, while using standard BDD techniques this problem is infeasible. Generally, BEDs are useful in applications, for example tautology checking, where the endresult as a reduced ordered BDD is small.
The formal verification of a pipelined doubleprecision IEEE floatingpoint multiplier
 In ICCAD
, 1995
"... Floatingpoint circuits are notoriously difficult to design and verify. For verification, simulation barely offers adequate coverage, conventional modelchecking techniques are infeasible, and theoremproving based verification is not sufficiently mature. In this paper we present the formal verifica ..."
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Cited by 39 (2 self)
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Floatingpoint circuits are notoriously difficult to design and verify. For verification, simulation barely offers adequate coverage, conventional modelchecking techniques are infeasible, and theoremproving based verification is not sufficiently mature. In this paper we present the formal verification of a radixeight, pipelined, IEEE doubleprecision floatingpoint multiplier. The verification was carried out using a mixture of modelchecking and theoremproving techniques in the Voss hardware verification system. By combining modelchecking and theoremproving we were able to build on the strengths of both areas and achieve significant results with a reasonable amount of effort. 1
Bisimulation Algorithms for Stochastic Process Algebras and their BDDbased Implementation
 In ARTS, LNCS 1601
, 1999
"... . Stochastic process algebras have been introduced in order to enable compositional performance analysis. The size of the state space is a limiting factor, especially if the system consists of many cooperating components. To fight state space explosion, various proposals for compositional aggregatio ..."
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Cited by 35 (13 self)
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. Stochastic process algebras have been introduced in order to enable compositional performance analysis. The size of the state space is a limiting factor, especially if the system consists of many cooperating components. To fight state space explosion, various proposals for compositional aggregation have been made. They rely on minimisation with respect to a congruence relation. This paper addresses the computational complexity of minimisation algorithms and explains how efficient, BDDbased data structures can be employed for this purpose. 1 Introduction Compositional application of stochastic process algebras (SPA) is particularly successful if the system structure can be exploited during Markov chain generation. For this purpose, congruence relations have been developed which justify minimisation of components without touching behavioural properties. Examples of such relations are strong equivalence [22], (strong and weak) Markovian bisimilarity [16] and extended Markovian bisimi...
A lower bound for integer multiplication with readonce branching programs
 SIAM Journal on Computing
, 1998
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Binary decision diagrams in theory and practice
, 2001
"... Decision diagrams (DDs) are the stateoftheart data structure in VLSI CAD and have been successfully applied in many other fields.DDs are widely used and are also integrated in commercial tools.This special section comprises six contributed articles on various aspects of the theory and application ..."
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Cited by 31 (7 self)
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Decision diagrams (DDs) are the stateoftheart data structure in VLSI CAD and have been successfully applied in many other fields.DDs are widely used and are also integrated in commercial tools.This special section comprises six contributed articles on various aspects of the theory and application of DDs.As preparation for these contributions, the present article reviews the basic definitions of binary decision diagrams (BDDs). We provide a brief overview and study theoretical and practical aspects.Basic properties of BDDs are discussed and manipulation algorithms are described.Extensions of BDDs are investigated and by this we give a deeper insight into the basic data structure.Finally we outline several applications of BDDs and their extensions and suggest a number of articles and books for those who wish to pursue the topic in more depth.