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Efficient modeling of memory arrays in symbolic ternary simulation,” in TACAS, (1998)

by M N Velev, R E Bryant
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An Industrially Effective Environment for Formal Hardware Verification

by C-J H Seger, R B Jones, J W O’Leary, T F Melham, M Aagaard, C Barrett, D Syme - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems , 2005
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...vior for an AND gate. Symbolic indexing finds its greatest utility in verification of regular memory structures, as it significantly reduces the number of BDD variables required to encode data values =-=[44]-=-–[46]. Consider an n × m-bit memory M with n rows and m bits per row, i.e., the memory is accessed with a log 2 n-bit address and returns m bits of data. Suppose that whether the memory correctly stor...

Exploiting Positive Equality and Partial Non-Consistency in the Formal Verification of Pipelined Microprocessors

by Miroslav N. Velev, Randal E. Bryant - In Design Automation Conference , 1999
"... We study the applicability of the logic of Positive Equality with Uninterpreted Functions (PEUF) [2][3] to the verification of pipelined microprocessors with very large Instruction Set Architectures (ISAs). Abstraction of memory arrays and functional units is employed, while the control logic of the ..."
Abstract - Cited by 15 (9 self) - Add to MetaCart
We study the applicability of the logic of Positive Equality with Uninterpreted Functions (PEUF) [2][3] to the verification of pipelined microprocessors with very large Instruction Set Architectures (ISAs). Abstraction of memory arrays and functional units is employed, while the control logic of the processors is kept intact from the original gate-level designs. PEUF is an extension of the logic of Equality with Uninterpreted Functions, introduced by Burch and Dill [4], that allows us to use distinct constants for the data operands and instruction addresses needed in the symbolic expression for the correctness criterion. We present several techniques that make PEUF scale very efficiently for the verification of pipelined microprocessors with large ISAs. These techniques are based on allowing a limited form of non-consistency in the uninterpreted functions, representing initial memory state and ALU behaviors. Our tool required less than 30 seconds of CPU time and 5 MB of memory to verif...
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...ons implemented in the processor. In modeling of microprocessors, we use abstraction of memory arrays and functional units. We achieve the abstraction by means of the Efficient Memory Model (EMM) [13]=-=[14]-=- and its capability to dynamically introduce new initial state (as required by a simulation sequence) which is consistent with previously introduced initial state. Observing that every combinational b...

TLSim and EVC: a term-level symbolic simulator and an efficient decision procedure for the logic of equality with uninterpreted functions and memories

by Miroslav N. Velev, Randal E. Bryant - Int. J. Embedded Systems , 2005
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Verification of Pipelined Microprocessors by Correspondence Checking in Symbolic Ternary Simulation

by Miroslav N. Velev, Randal E. Bryant , 1998
"... This paper makes the idea of memory shadowing [5] applicable to symbolic ternary simulation. Memory shadowing, an extension of Burch and Dill's pipeline verification method [6] to the bit level, is a technique for providing on-the-fly identical initial memory state to two different memory execu ..."
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This paper makes the idea of memory shadowing [5] applicable to symbolic ternary simulation. Memory shadowing, an extension of Burch and Dill's pipeline verification method [6] to the bit level, is a technique for providing on-the-fly identical initial memory state to two different memory execution sequences. We also present an algorithm which compares the final states of two memories for ternary correspondence, as well as an approach for generating efficiently the initial state of memories. These techniques allow us to verify that a pipelined circuit has behavior corresponding to that of its unpipelined specification by simulating two symbolic ternary execution sequences and comparing their final memory states. Experimental results show the potential of the new ideas. 1. Introduction This paper makes memory shadowing [5] applicable to symbolic ternary simulation. Memory shadowing is a technique for providing on-the-fly identical initial memory state to two different memory execution ...

Coping with Moore’s law (and more): Supporting arrays in state-of-the-art model checkers

by Jason Baumgartner , Michael Case , Hari Mony - in Formal Methods in Computer-Aided Design 2010
"... Abstract-State-of-the-art hardware model checkers and equivalence checkers rely upon a diversity of synergistic algorithms to achieve adequate scalability and automation. While higher-level decision procedures have enhanced capacity for problems of amenable syntax, little prior work has addressed ( ..."
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Abstract-State-of-the-art hardware model checkers and equivalence checkers rely upon a diversity of synergistic algorithms to achieve adequate scalability and automation. While higher-level decision procedures have enhanced capacity for problems of amenable syntax, little prior work has addressed (1) the generalization of many critical synergistic algorithms beyond bit-blasted representations, nor (2) the issue of bridging higherlevel techniques to problems of complex circuit-accurate syntax. In this paper, we extend a variety of bit-level algorithms to designs with memory arrays, and introduce techniques to rewrite arrays from circuit-accurate to verification-amenable behavioral syntax. These extensions have numerous motivations, from scaling formal methods to verify ever-growing design components, to enabling hardware model checkers to reason about software-like systems, to allowing state-of-the-art model checkers to support temporallyconsistent function-and predicate-abstraction.
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...presentation. Substantial recent research has focused upon enhanced reasoning scalability for designs expressed at a higher-level of abstraction. For example, numerous techniques have been established to enhance the verification scalability of designs containing arrays: storage devices arranged as a set of addressable rows of a specific width, accessed through atomic write and read operations. Example techniques include the efficient memory model which preserves data consistency within temporally-bounded reasoning using a modeling whose complexity grows sub-linearly with respect to array size [8], [9], and the abstraction-refinement technique of [10] which reduces an array to a small number of consistently-modeled rows. Additionally, a large number of dedicated decision procedures have been developed around theories of arrays [11]. While extremely powerful for amenable problems, such techniques have not yet delivered their full impact in industrial hardware verification for several reasons. First, such techniques are often applicable only to designs with behavioral syntax, not to designs of intricate circuit-accurate syntax. Manual creation of behavioral models may alleviate this conc...

Handling Special Constructs in Symbolic Simulation

by Alfred Kölbl, James Kukula, Kurt Antreich, Robert Damiano - 39th Design Automation Conference (DAC ’02 , 2002
"... Symbolic simulation is a formal verification technique which combines the flexibility of conventional simulation with powerful symbolic methods. Some constructs, however, which are easy to handle in conventional simulation need special consideration in symbolic simulation. This paper discusses some ..."
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Symbolic simulation is a formal verification technique which combines the flexibility of conventional simulation with powerful symbolic methods. Some constructs, however, which are easy to handle in conventional simulation need special consideration in symbolic simulation. This paper discusses some special constructs that require unique treatment in symbolic simulation such as the symbolic representation of arrays, an efficient symbolic method for storing arrayed instances and the handling of symbolic data-dependent delays. We present results which demonstrate the effectiveness of our symbolic array model in the simulation of highly regular structures like FPGAs, memories or cellular automata.
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...usually only a very small portion of the array is accessed, arrays of virtually any size can be realized. The idea of a sparse representation of large arrays in symbolic simulation is also subject of =-=[12, 14]-=-. In that work, Velev and Bryant propose to store symbolic accesses to a memory in a list containing entries of the form (c, i, d), where c is a Boolean expression denoting the set of conditions for w...

Incorporating Timing Constraints in the Efficient Memory Model for Symbolic Ternary Simulation

by Incorporating Timing Constraints, Miroslav N. Velev, Randal E. Bryant
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