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158
Symbolic model checking for sequential circuit verification
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 1994
"... The temporal logic model checking algorithm of Clarke, Emerson, and Sistla [17] is modified to represent state graphs using binary decision diagrams (BDD’s) [7] and partitioned trunsirion relations [lo], 1111. Because this representation captures some of the regularity in the state space of circuit ..."
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Cited by 239 (11 self)
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The temporal logic model checking algorithm of Clarke, Emerson, and Sistla [17] is modified to represent state graphs using binary decision diagrams (BDD’s) [7] and partitioned trunsirion relations [lo], 1111. Because this representation captures some of the regularity in the state space of circuits with data path logic, we are able to verify circuits with an extremely large number of states. We demonstrate this new technique on a synchronous pipelined design with approximately 5 x 10^120 states. Our model checking algorithm handles full CTL with fairness constraints. Consequently, we are able to express a number of important liveness and fairness properties, which would otherwise not be expressible in CTL. We give empirical results on the performance of the algorithm applied to both synchronous and asynchronous circuits with data path logic.
Better Verification Through Symmetry
, 1996
"... A fundamental difficulty in automatic formal verification of finitestate systems is the state explosion problem  even relatively simple systems can produce very large state spaces, causing great difficulties for methods that rely on explicit state enumeration. We address the problem by exploiting ..."
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Cited by 196 (8 self)
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A fundamental difficulty in automatic formal verification of finitestate systems is the state explosion problem  even relatively simple systems can produce very large state spaces, causing great difficulties for methods that rely on explicit state enumeration. We address the problem by exploiting structural symmetries in the description of the system to be verified. We make symmetries easy to detect by introducing a new data type scalarset, a finite and unordered set, to our description language. The operations on scalarsets are restricted so that states are guaranteed to have the same future behaviors, up to permutation of the elements of the scalarsets. Using the symmetries implied by scalarsets, a verifier can automatically generate a reduced state space, on the fly. We provide a proof of the soundness of the new symmetrybased verification algorithm based on a definition of the formal semantics of a simple description language with scalarsets. The algorithm has been implemented ...
Symbolic Model Checking with Partitioned Transition Relations
, 1991
"... We significantly reduce the complexity of BDDbased symbolic verification by using partitioned transition relations to represent state transition graphs. This method can be applied to both synchronous and asynchronous circuits. The times necessary to verify a synchronous pipeline and an asynchronous ..."
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Cited by 166 (16 self)
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We significantly reduce the complexity of BDDbased symbolic verification by using partitioned transition relations to represent state transition graphs. This method can be applied to both synchronous and asynchronous circuits. The times necessary to verify a synchronous pipeline and an asynchronous stack are both bounded by a low polynomial in the size of the circuit. We were able to handle stacks with over 10 50 reachable states and pipelines with over 10 120 reachable states. 1 Introduction Although methods for verifying sequential circuits by searching their state transition graphs have been investigated for many years, it is only recently that such methods have begun to seem practical. Before, the largest circuits that could be verified had about 10 6 states. Now it is easy to check circuits that have many orders of magnitude more states [3, 5, 6, 7]. The reason for the dramatic increase is the use of special data structures such as binary decision diagrams (BDDs) [2] for...
NUSMV: a new symbolic model checker
 International Journal on Software Tools for Technology Transfer
, 2000
"... This paper describes a new symbolic model checker, called NUSMV, developed as part of a joint project between CMU and IRST. NUSMV is the result of the reengineering, reimplementation, and, to a limited extent, extension of the CMU SMV model checker. The core of this paper consists of a detailed de ..."
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Cited by 130 (18 self)
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This paper describes a new symbolic model checker, called NUSMV, developed as part of a joint project between CMU and IRST. NUSMV is the result of the reengineering, reimplementation, and, to a limited extent, extension of the CMU SMV model checker. The core of this paper consists of a detailed description of the NUSMV functionalities, architecture, and implementation.
Multiway Decision Graphs for Automated Hardware Verification
, 1996
"... Traditional ROBDDbased methods of automated verification suffer from the drawback that they require a binary representation of the circuit. To overcome this limitation we propose a broader class of decision graphs, called Multiway Decision Graphs (MDGs), of which ROBDDs are a special case. With MDG ..."
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Cited by 80 (14 self)
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Traditional ROBDDbased methods of automated verification suffer from the drawback that they require a binary representation of the circuit. To overcome this limitation we propose a broader class of decision graphs, called Multiway Decision Graphs (MDGs), of which ROBDDs are a special case. With MDGs, a data value is represented by a single variable of abstract type, rather than by 32 or 64 boolean variables, and a data operation is represented by an uninterpreted function symbol. MDGs are thus much more compact than ROBDDs, and this greatly increases the range of circuits that can be verified. We give algorithms for MDG manipulation, and for implicit state enumeration using MDGs. We have implemented an MDG package and provide experimental results.
Efficient BDD Algorithms for FSM Synthesis and Verification
 In IEEE/ACM Proceedings International Workshop on Logic Synthesis, Lake Tahoe (NV
, 1995
"... We describe a set of BDD based algorithms for efficient FSM synthesis and verification. We establish that the core computation in both synthesis and verification is forming the image and preimage of sets of states under the transition relation characterizing the design. To make these steps as effic ..."
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Cited by 69 (2 self)
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We describe a set of BDD based algorithms for efficient FSM synthesis and verification. We establish that the core computation in both synthesis and verification is forming the image and preimage of sets of states under the transition relation characterizing the design. To make these steps as efficient as possible, we address BDD variable ordering, use of partitioned transition relations, and use of clustering. We provide an integrated set of algorithms and give references and comparisons with previous work. We report experimental results on a series of seven industrial examples containing from 28 to 172 binary valued latches. 1 Introduction The advent of modern VLSI CAD tools has radically changed the process of designing digital systems. The first CAD tools automated the final stages of design, such as placement and routing. As the low level steps became better understood, the focus shifted to the higher stages. In particular logic synthesis, the science of optimizing designs (for ...
Fast functional simulation using branching programs
 In Proceedings of the IEEE International Conference on ComputerAided Design
, 1995
"... This paper addresses the problem of speeding up functional (delayindependent) logic simulation for synchronous digital systems. The problem needs very little new motivation – cyclebased functional simulation is the largest consumer of computing cycles in system design. Most existing simulators for ..."
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Cited by 64 (0 self)
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This paper addresses the problem of speeding up functional (delayindependent) logic simulation for synchronous digital systems. The problem needs very little new motivation – cyclebased functional simulation is the largest consumer of computing cycles in system design. Most existing simulators for this task can be classified as being either event driven or levelized compiledcode, with the levelized compiled code simulators generally being considered faster for this task. An alternative technique, based on evaluation using branching programs, was suggested about a decade ago in the context of switch level functional simulation. However, this had very limited application since it could not handle the large circuits encountered in practice. This paper resurrects the basic idea present this technique and provides significant modifications that enable its application to contemporary industrial strength circuits. We present experimental results that demonstrate up to a 10X speedup over levelized compiled code simulation for a large suite of benchmark circuits as well as for industrial examples with over 40,000 gates. 1
Automatic Generation of Functional Vectors Using The Extended Finite State Machine Model
 ACM Trans. on design Automation of Electronic Systems
, 1996
"... We present a method of automatic generation of functional vectors for sequential circuits. These vectors can be used for design verification, manufacturing testing or power estimation. A highlevel description of the circuit, in VHDL or C, is assumed available. Our method automatically transforms th ..."
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Cited by 51 (2 self)
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We present a method of automatic generation of functional vectors for sequential circuits. These vectors can be used for design verification, manufacturing testing or power estimation. A highlevel description of the circuit, in VHDL or C, is assumed available. Our method automatically transforms the highlevel description, in VHDL or C, of a circuit into an extended finite state machine (EFSM) model that is used to generate functional vectors. The EFSM model is a generalization of the traditional state machine model. It is a compact representation of models with local data variables and preserves many nice properties of a traditional state machine model. The theoretical background of the EFSM model will be addressed in this paper. Our method guarantees that the generated vectors cover every statement in the highlevel description at least once. Experimental results show that a set of comprehensive functional vectors for sequential circuits with more than a hundred flipflops can be ge...
Heuristic minimization of BDDs using don’t cares
 In Proceedings of the Design Automation Conference
, 1994
"... We present heuristic algorithms for finding a minimum BDD size cover of an incompletely specified function, assuming the variable ordering is fixed. In some algorithms based on BDDs, incompletely specified functions arise for which any cover of the function will suffice. Choosing a cover that has a ..."
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Cited by 44 (6 self)
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We present heuristic algorithms for finding a minimum BDD size cover of an incompletely specified function, assuming the variable ordering is fixed. In some algorithms based on BDDs, incompletely specified functions arise for which any cover of the function will suffice. Choosing a cover that has a small BDD representation may yield significant performance gains. We present a systematic study of this problem, establishing a unified framework for heuristic algorithms, proving optimality in some cases,and presenting experimental results. 1
BDD variable ordering for interacting finite state machines
 IN PROC. OF THE DESIGN AUTOMATION CONF
, 1994
"... We address the problem of obtaining good variable orderings for the BDD representation of a system of interacting finite state machines (FSMs). Orderings are derived from the communication structure of the system. Communication complexity arguments are used to prove upper bounds on the size of the B ..."
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Cited by 43 (7 self)
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We address the problem of obtaining good variable orderings for the BDD representation of a system of interacting finite state machines (FSMs). Orderings are derived from the communication structure of the system. Communication complexity arguments are used to prove upper bounds on the size of the BDD for the transition relation of the product machine in terms of the communication graph, and optimal orderings are exhibited for a variety of regular systems. Based on the bounds we formulate algorithms for variable ordering. We perform reached state analysis on a number of standard verification benchmarks to test the effectiveness of our ordering strategy; experimental results demonstrate the e cacy of our approach. The algorithms described in this paper have been implemented in HSIS, a hierarchical synthesis and verification tool currently under development at Berkeley.