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Modular verification of timed circuits using automatic abstraction (2003)

by H Zheng, E Mercer, C J Myers
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Synthesis of speed independent circuits based on decomposition

by Tomohiro Yoneda - In ASYNC 2004 , 2004
"... This paper presents a decomposition method for speedindependent circuit design that is capable of significantly reducing the cost of synthesis. In particular, this method synthesizes each output individually. It begins by contracting the STG to include only transitions on the output of interest and ..."
Abstract - Cited by 9 (2 self) - Add to MetaCart
This paper presents a decomposition method for speedindependent circuit design that is capable of significantly reducing the cost of synthesis. In particular, this method synthesizes each output individually. It begins by contracting the STG to include only transitions on the output of interest and its trigger signals. Next, the reachable state space for this contracted STG is analyzed to determine a minimal number of additional signals which must be reintroduced into the STG to obtain CSC. The circuit for this output is then synthesized from this STG. Results show that the quality of the circuit implementation is nearly as good as the one found from the full reachable state space, but it can be applied to find circuits for which full state space methods cannot be successfully applied. The proposed method has been implemented as a part of our tool nutas (Nii-Utah Timed Asynchronous circuit Synthesis system), and its very first version is available at
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...sis. As for the first problem, Vogler and Wollowski recently formalized the contraction algorithm using a bisimulation relation in [15], and Zheng and Myers developed a timed contraction algorithm in =-=[16]-=-. On the other hand, Puri and Gu tried to solve the second problem in [17]. Their algorithm greedily removes an irrelevant signal (with respect to the output signal) such that the number of CSC confli...

On Timing Analysis of Combinational Circuits

by Ramzi Ben Salah, Marius Bozga, Oded Maler - In FORMATS’03, LNCS 2791 , 2003
"... Abstract. In this paper we report some progress in applying timed automata technology to large-scale problems. We focus on the problem of finding maximal stabilization time for combinational circuits whose inputs change only once and hence they can be modeled using acyclic timed automata. We develop ..."
Abstract - Cited by 9 (1 self) - Add to MetaCart
Abstract. In this paper we report some progress in applying timed automata technology to large-scale problems. We focus on the problem of finding maximal stabilization time for combinational circuits whose inputs change only once and hence they can be modeled using acyclic timed automata. We develop a “divideand-conquer” methodology based on decomposing the circuit into sub-circuits and using timed automata analysis tools to build conservative low-complexity approximations of the sub-circuits to be used as inputs for the rest of the system. Some preliminary results of this methodology are reported. 1
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...ed automata, which is used later to verify a multi-stage asynchronous circuit [TB97] by using small abstractions for each stage. These abstractions are generated manually. The closest work to ours is =-=[ZMM03] which use-=-s timed Petri nets for describing circuits and their desired properties. To abstract a circuit they apply "safe transformations" that consist of hiding of internal actions and clocks, and po...

Verification of timed circuits with failure directed abstractions

by Hao Zheng, Chris J. Myers, Senior Member, David Walter, Student Member, Scott Little, Tomohiro Yoneda - In 21st International Conference on Computer Design (ICCD , 2003
"... Abstract — This paper presents a method to address state explosion in timed circuit verification by using abstraction directed by the failure model. This method allows us to decompose the verification problem into a set of subproblems, each of which proves that a specific failure condition does not ..."
Abstract - Cited by 7 (4 self) - Add to MetaCart
Abstract — This paper presents a method to address state explosion in timed circuit verification by using abstraction directed by the failure model. This method allows us to decompose the verification problem into a set of subproblems, each of which proves that a specific failure condition does not occur. To each subproblem, abstraction is applied using safe transformations to reduce the complexity of verification. The abstraction preserves all essential behaviors conservatively for the specific failure model in the concrete description. Therefore, no violations of the given failure model are missed when only the abstract description is error trace to either find a concrete error trace or report that it is a false negative. This paper presents results using the proposed failure directed abstractions as applied to several large timed circuit designs. Index Terms — timed circuits, formal verification, abstraction. I.
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...te abstraction can be combined with our method to further improve performance. A method that combines compositional reasoning and abstraction to reduce the cost of timing verification is presented in =-=[29]-=-. By utilizing the inherent modular structure in hardware designs, each module in a design is verified individually. Before verification, information in the environment that is irrelevant to reasoning...

Automatic abstraction for verification of cyber-physical systems

by Robert A. Thacker, Kevin R. Jones, Chris J. Myers, Hao Zheng - In Proc. of ICCPS , 2010
"... Models of cyber-physical systems are inherently complex since they must represent hardware, software, and the physi-cal environment. Formal verification of these models is often precluded by state explosion. Fortunately, many important properties may only depend upon a relatively small portion of th ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
Models of cyber-physical systems are inherently complex since they must represent hardware, software, and the physi-cal environment. Formal verification of these models is often precluded by state explosion. Fortunately, many important properties may only depend upon a relatively small portion of the system being accurately modeled. This paper presents an automatic abstraction methodology that simplifies the model accordingly. Preliminary results on a fault-tolerant temperature sensor are encouraging.
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...ansformations to remove details from the model that are irrelevant to the property of interest. These transformations are inspired by transformations for ordinary Petri nets [11] and timed Petri nets =-=[15]-=-. They are also inspired from various static analysis techniques used by compilers [1]. Other related work includes reduction techniques for timed and hybrid automata described in [6, 7, 10]. This pap...

Efficient verification of hazard-freedom in gate-level timed asynchronous circuits

by Curtis A. Nelson, Chris J. Myers, Tomohiro Yoneda - IEEE Transactions on CAD, page
"... This paper presents an efficient method for verifying hazard freedom in timed asynchronous circuits. Timed circuits are a class of asynchronous circuits that utilize explicit timing information for optimization throughout the entire design process. In asynchronous circuits, correct operation require ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
This paper presents an efficient method for verifying hazard freedom in timed asynchronous circuits. Timed circuits are a class of asynchronous circuits that utilize explicit timing information for optimization throughout the entire design process. In asynchronous circuits, correct operation requires that there are no hazards in the circuit implementation. Therefore, when designing an asynchronous circuit, each internal node and output of the circuit must be verified for hazard-freedom to ensure correct operation. Current verification algorithms for timed asynchronous circuits require an explicit state exploration often resulting in state explosion for even modest sized examples. The goal of this work is to abstract the behavior of internal nodes and utilize this information to make a conservative determination of hazard-freedom for each node in the circuit. Experimental results indicate that this approach is substantially more efficient than existing timing verification tools. These results also indicate that this method scales well for large examples. It is capable of analyzing circuits in less than a second that could not be previously analyzed. While this method is conservative in that some false hazards may be reported, our results indicate that the number of false hazards is small. 1.
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...ique has the potential to substantially reduce the complexity of verification as demonstrated in the results shown in [2]. Abstraction of internal nodes to combat state explosion is also performed in =-=[20, 19]-=-. This work, however, is not directed at verification of hazard-freedom and requires the use of Timed Petri Nets for all design descriptions including the gates to be analyzed. While it is potentially...

Synthesis of Timed Circuits Based on Decomposition

by Tomohiro Yoneda, Chris J. Myers, Senior Member
"... Abstract—This paper presents a decomposition-based method for timed circuit design that is capable of significantly reducing the cost of synthesis. In particular, this method synthesizes each output individually. It begins by contracting the timed signal transition graph (STG) to include only transi ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
Abstract—This paper presents a decomposition-based method for timed circuit design that is capable of significantly reducing the cost of synthesis. In particular, this method synthesizes each output individually. It begins by contracting the timed signal transition graph (STG) to include only transitions on the output of interest and its possible trigger signals. Next, the reachable state space for this contracted STG is analyzed to determine a minimal number of additional signals, which must be reintroduced into the STG to obtain complete state coding. The circuit for this output is then synthesized from this STG. Results show that the quality of the circuit implementation is nearly as good as the one found from the full reachable state space, but it can be applied to find circuits for which full-state-space methods cannot be successfully applied. The proposed method has been implemented as a part of our tool Nii-Utah Timed Asynchronous circuit Synthesis system (nutas), and its first version is available at
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...thesis. As for the first problem, Vogler and Wollowski recently formalized the contraction algorithm using a bisimulation relation in [18], and Zheng et al. developed a timed-contraction algorithm in =-=[19]-=-. On the other hand, Puri and Gu tried to solve the second problem in [20]. Their algorithm greedily removes an irrelevant signal (with respect to the output signal) such that the number of CSC violat...

Verifying Synchronization Strategies

by Chris J. Myers, Eric Mercer, Hans Jacobson
"... Abstract. Over the years, there have been numerous methods proposed to solve the synchronization problem. Many of these methods, however, are not sufficiently evaluated before being utilized leading to problems in a system design that are difficult to diagnose and solve. Therefore, it is crucial tha ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
Abstract. Over the years, there have been numerous methods proposed to solve the synchronization problem. Many of these methods, however, are not sufficiently evaluated before being utilized leading to problems in a system design that are difficult to diagnose and solve. Therefore, it is crucial that strategies for synchronization are critically analyzed and verified before being incorporated in a system design. This paper reviews a number of the known methods for synchronization, discusses issues in their design, and presents techniques for their verification. 1 The Synchronization Problem While there have been many promising asynchronous design examples [48,4, 17,42,1], asynchronous design is still not seeing widespread use. One important reason for this is that asynchronous designs must communicate with other parts of the system which typically operate synchronously. Unfortunately, this is difficult to do reliably without substantial latency penalties. When this latency penalty is taken into account, most, if not all, of the performance advantage gained by an asynchronous design is lost. Even if no asynchronous modules are used, synchronous modules operating at different clock rates or out of phase can have the same problem. The latter problem is becoming more significant as it becomes increasingly difficult to distribute a single global clock to all parts of the chip. Many designers today are considering the necessity of having multiple
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...ipeline in Figure 13 is shown in Figure 14. There are four processes in this figure. Figure 14(a) models the latch to generate stall2 based on its input stall3. Figure 14(b) models stallsclk ∧ stall3 =-=[40, 50]-=- stall2 − stall2+ [40, 50] clk ∧ ¬stall3 ¬stall2 [0, ∞] nstall2 − nstall2+ [0, ∞] stall2 (a) (b) clk ∧ nstall2 [35, 45] clk2 − clk2+ [35, 45] ¬clk ∨ ¬nstall2 clk2 ∧ d1 [40, 50] d2 − d2+ [40, 50] clk2 ...

ABSTRACT On Timed Components and their Abstraction

by Ramzi Ben Salah
"... We develop a new technique for generating small-complexity abstractions of timed automata that provide an approximation of their timed input-output behavior. This abstraction is obtained by first augmenting the automaton with additional input clocks, computing the “reachable ” timed automaton that c ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We develop a new technique for generating small-complexity abstractions of timed automata that provide an approximation of their timed input-output behavior. This abstraction is obtained by first augmenting the automaton with additional input clocks, computing the “reachable ” timed automaton that corresponds to the augmented model and finally “hiding ” the internal variables and clocks of the system. As a result we obtain a timed automaton that does not allow any qualitative behavior which is infeasible due to timing constraints, and which maintains a relaxed form of the timing constraints associated with the feasible behaviors. We have implemented this technique and applied it to several examples from different application domains.
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...rule we obtain the automaton of Figure 7 which is nothing but a demonstration of the following equivalence on delay operators: D[1,2](D[1,2](x)) = D[2,4](x). A similar transformation was presented in =-=[11]-=- for timed Petri nets. The situation gets more complicated when the system admits more parallelism and input events may appear more frequently. We have developed a variety of minimization algorithms t...

A compositional Minimization Approach for Large Asynchronous Design Verification

by Hao Zheng, Emmanuel Rodriguez, Yingying Zhang, Chris Myers
"... Abstract. This paper presents a compositional minimization approach with efficient state space reductions for verifying non-trivial asynchronous designs. These reductions can result in a reduced model that contains the exact same set of observably equivalent behavior in the original model, therefore ..."
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Abstract. This paper presents a compositional minimization approach with efficient state space reductions for verifying non-trivial asynchronous designs. These reductions can result in a reduced model that contains the exact same set of observably equivalent behavior in the original model, therefore no false counter-examples are produced at the end of verification on the reduced model. This approach allows designs that cannot be handled monolithically or with partial-order reduction to be verified without difficulty. The experimental results show significant scale-up of the compositional minimization approach using these reductions on a number of large asynchronous designs.
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...e concrete model. This can be very time-consuming. If reduction is too conservative, the number of false errors may become too excessive, and checking these false errors can become the bottleneck. In =-=[22,27,28]-=-, methods are described for compositionally verifying asynchronous designs based on Petri-net reduction. These methods simplify Petri-net models of asynchronous designs either following the design par...

1 Efficient Verification of Hazard-Freedom in Gate-Level Timed Asynchronous Circuits

by Curtis A. Nelson, Chris J. Myers, Senior Member, Tomohiro Yoneda
"... Abstract — This article presents an efficient method for verifying hazard freedom in gate-level timed asynchronous circuits. Timed circuits are a class of asynchronous circuits that are optimized using explicit timing information. In asynchronous circuits, correct operation requires that there are n ..."
Abstract - Add to MetaCart
Abstract — This article presents an efficient method for verifying hazard freedom in gate-level timed asynchronous circuits. Timed circuits are a class of asynchronous circuits that are optimized using explicit timing information. In asynchronous circuits, correct operation requires that there are no hazards in the circuit implementation. Therefore, when designing an asynchronous circuit, each internal node and output of the circuit must be verified for hazard-freedom to ensure correct operation. Current verification algorithms for timed circuits require an explicit state exploration often resulting in state explosion for even modest sized examples. The goal of this work is to abstract the behavior of internal nodes and utilize this information to make a conservative determination of hazard-freedom for each node in the circuit. Experimental results indicate that this approach is substantially more efficient than existing timing verification tools. These results also indicate that this method scales well for large examples in that it is capable of analyzing circuits in less than a second that could not be previously analyzed. While this method is conservative in that some false hazards may be reported, our results indicate that their number is small. Index Terms — Verification, hazard-freedom, timed asynchronous circuits, technology mapping
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...ue has the potential to substantially reduce the complexity of verification as demonstrated in the results shown in [10]. Abstraction of internal nodes to combat state explosion is performed in [15], =-=[16]-=-. This work, however, is not directed at verification of hazard-freedom and requires the use of timed Petri Nets for all design descriptions including the gates to be analyzed. This work could potenti...

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