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38
Formal verification in hardware design: A survey
, 1997
"... In recent years, formal methods have emerged as an alternative approach to ensuring the quality and correctness of hardware designs, overcoming some of the limitations of traditional validation techniques such as simulation and testing. There are two main aspects to the application of formal methods ..."
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Cited by 113 (0 self)
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In recent years, formal methods have emerged as an alternative approach to ensuring the quality and correctness of hardware designs, overcoming some of the limitations of traditional validation techniques such as simulation and testing. There are two main aspects to the application of formal methods in a design process: The formal framework used to specify desired properties of a design, and the verification techniques and tools used to reason about the relationship between a specification and a corresponding implementation. We survey a variety of frameworks and techniques which have been proposed in the literature and applied to actual designs. The specification frameworks we describe include temporal logics, predicate logic, abstraction and refinement, as well as containment between!regular languages. The verification techniques presented include model checking, automatatheoretic techniques, automated theorem proving, and approaches that integrate the above methods.
Formal Verification by Symbolic Evaluation of PartiallyOrdered Trajectories
 Formal Methods in System Design
, 1993
"... Symbolic trajectory evaluation provides a means to formally verify properties of a sequential system by a modified form of symbolic simulation. The desired system properties are expressed in a notation combining Boolean expressions and the temporal logic "nexttime" operator. In its sim ..."
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Cited by 107 (24 self)
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Symbolic trajectory evaluation provides a means to formally verify properties of a sequential system by a modified form of symbolic simulation. The desired system properties are expressed in a notation combining Boolean expressions and the temporal logic "nexttime" operator. In its simplest form, each property is expressed as an assertion [A =) C], where the antecedent A expresses some assumed conditions on the system state over a bounded time period, and the consequent C expresses conditions that should result. A generalization allows simple invariants to be established and proven automatically. The verifier operates on system models in which the state space is ordered by "information content". By suitable restrictions to the specification notation, we guarantee that for every trajectory formula, there is a unique weakest state trajectory that satisfies it. Therefore, we can verify an assertion [A =) C] by simulating the system over the weakest trajectory for A and testing...
An Industrially Effective Environment for Formal Hardware Verification
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 2005
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Formal Hardware Verification with BDDs: An Introduction
"... This paper is a brief introduction to the main paradigms for using BDDs in formal hardware verification. The paper addresses two audiences: for people doing theoretical BDD research, the paper gives a glimpse of the problems in the main application area, and ..."
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Cited by 27 (0 self)
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This paper is a brief introduction to the main paradigms for using BDDs in formal hardware verification. The paper addresses two audiences: for people doing theoretical BDD research, the paper gives a glimpse of the problems in the main application area, and
Symbolic Trajectory Evaluation
 Formal Hardware Verification
, 1996
"... ion The main problem with model checking is the state explosion problem  the state space grows exponentially with system size. Two methods have some popularity in attacking this problem: compositional methods and abstraction. While they cannot solve the problem in general, they do offer significa ..."
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Cited by 27 (6 self)
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ion The main problem with model checking is the state explosion problem  the state space grows exponentially with system size. Two methods have some popularity in attacking this problem: compositional methods and abstraction. While they cannot solve the problem in general, they do offer significant improvements in performance. The direct method of verifying that a circuit has a property f is to show the model M satisfies f . The idea behind abstraction is that instead of verifying property f of model M , we verify property f A of model MA and the answer we get helps us answer the original problem. The system MA is an abstraction of the system M . One possibility is to build an abstraction MA that is equivalent (e.g. bisimilar [48]) to M . This sometimes leads to performance advantages if the state space of MA is smaller than M . This type of abstraction would more likely be used in model comparison (e.g. as in [38]). Typically, the behaviour of an abstraction is not equivalent...
Binary Decision Diagrams on Network of Workstations
 Proc. of International Conference on Computer Design (ICCD'96
, 1996
"... The success of all binary decision diagram (BDD) based synthesis and verification algorithms depend on the ability to efficiently manipulate very large BDDs. We present algorithms for manipulation of very large Binary Decision Diagrams (BDDs) on a network of workstations (NOW). ANOW provides a colle ..."
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Cited by 26 (0 self)
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The success of all binary decision diagram (BDD) based synthesis and verification algorithms depend on the ability to efficiently manipulate very large BDDs. We present algorithms for manipulation of very large Binary Decision Diagrams (BDDs) on a network of workstations (NOW). ANOW provides a collection of main memories and disks which can be used effectively to create and manipulate very large BDDs. To make efficient use of memory resources of a NOW, while completing execution in a reasonable amount of wall clock time, extension of breadthfirst technique is used to manipulate BDDs. BDDs are partitioned such that nodes for a set of consecutive variables are assigned to the same workstation. We present experimental results to demonstrate the capability of such an approach and point towards the potential impact for manipulating very large BDDs. 1 Introduction The manipulation of boolean functions is one of the most important operations in several areas of computeraided design such a...
High Performance BDD Package Based on Exploiting Memory Hierarchy
, 1996
"... The success of binary decision diagram (BDD) based algorithms for synthesis and/or verification depend on the availability of a high performance package to manipulate very large BDDs. Stateofthe art BDD packages, based on the conventional depthfirst technique, limit the size of the BDDs due to a ..."
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Cited by 20 (3 self)
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The success of binary decision diagram (BDD) based algorithms for synthesis and/or verification depend on the availability of a high performance package to manipulate very large BDDs. Stateofthe art BDD packages, based on the conventional depthfirst technique, limit the size of the BDDs due to a disorderly memory access patterns that results in unacceptably high elapsed time when the BDD size exceeds the main memory capacity. We present a high performance BDD package that enables manipulation of very large BDDs by using an iterative breadthfirst technique directed towards localizing the memory accesses to exploit the memory system hierarchy. The new memoryoriented performance features of this package are 1) an architecture independent customized memory management scheme, 2) the ability to issue multiple independent BDD operations (superscalarity), and 3) the ability to perform multiple BDD operations even when the operands of some BDD operations are the result of some other operat...
FORMAL HARDWARE VERIFICATION BY SYMBOLIC TRAJECTORY EVALUATION
, 1997
"... Formal verification uses a set of languages, tools, and techniques to mathematically reason about the correctness of a hardware system. The form of mathematical reasoning is dependent upon the hardware system. This thesis concentrates on hardware systems that have a simple deterministic highlevel s ..."
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Cited by 18 (1 self)
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Formal verification uses a set of languages, tools, and techniques to mathematically reason about the correctness of a hardware system. The form of mathematical reasoning is dependent upon the hardware system. This thesis concentrates on hardware systems that have a simple deterministic highlevel specification but have implementations that exhibit highly nondeterministic behaviors. A typical example of such hardware systems are processors. At the high level, the sequencing model inherent in processors is the sequential execution model. The underlying implementation, however, uses features such as nondeterministic interface protocols, instruction pipelines, and multiple instruction issue which leads to nondeterministic behaviors. The goal is to develop a methodology with which a designer can show that a circuit fulfills the abstract specification of the desired system behavior. The abstract specification describes the highlevel behavior of the system independent of any timing or implementation details. The natural specification of a processor is the instruction set architecture. The specification is defined as a set of abstract assertions defining the effect of each operation on the uservisible state. An implementation mapping is used to relate abstract states to detailed circuit states. The mapping captures the microarchitecture of an implementation of the processor. Symbolic Trajectory Evaluation is used to verify that the circuit fulfills each individual abstract assertion under the implementation mapping. Symbolic Trajectory Evaluation can be considered to be a hybrid approach based on symbolic simulation and model checking algorithms. The methodology has been applied to the fixed point unit of a superscalar processor that implements the PowerPC architecture. The processor represents a significant leap of complexity compared to previous attempts at formal verification of processors. Our approach seems to be the first one that can truly deal with the complexity of pipeline interlocks.
Parametric Circuit Representation Using Inductive Boolean Functions
 In Computer Aided Verification, CAV '93, LNCS 697
, 1993
"... . We have developed a methodology based on symbolic manipulation of inductive Boolean functions (IBFs) for formal verification of inductivelydefined hardware. This methodology combines the techniques of reasoning by induction and symbolic tautologychecking in an automated and potentially efficient ..."
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Cited by 17 (2 self)
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. We have developed a methodology based on symbolic manipulation of inductive Boolean functions (IBFs) for formal verification of inductivelydefined hardware. This methodology combines the techniques of reasoning by induction and symbolic tautologychecking in an automated and potentially efficient way. In this paper, we describe a component of this methodology that regards various mechanisms used to represent inductivelydefined circuits in the form of IBFs. The focus is on general parameterization issues, such as multiple parameter functions, multiple output functions, interaction of different parameters for supporting compositions etc. These mechanisms, which may be useful in other applications involving parametric circuit descriptions, are illustrated through practical circuit examples along with preliminary results. We also describe an application of our formal verification methodology, where a proof by induction is performed by automatic symbolic manipulation of parametric circuit...
High performance bdd package by exploiting memory hierarchy
 In 33rd IEEE Design Automation Conference
, 1996
"... Abstract The success of binary decision diagram (BDD) ..."
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Cited by 16 (0 self)
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Abstract The success of binary decision diagram (BDD)