Scott Little

Verification of analog/mixed-signal circuits using labeled hybrid petri nets

System on a chip design results in the integration of digital, analog, and mixed-signal circuits on the same substrate which further complicates the already difficult validation problem. This paper presents a new model, labeled hybrid Petri nets (LHPNs), that is developed to be capable of modeling such a heterogeneous set of components. This paper also describes a compiler from VHDL-AMS to LHPNs. To support formal verification, this paper presents an efficient zone-based state space exploration algorithm for LHPNs. This algorithm uses a process known as warping to allow zones to describe continuous variables that may be changing at variable rates. Finally, this paper describes the application of this algorithm to a couple of analog/mixed-signal circuit examples

Analog MAP decoder for (8, 4) Hamming code in subthreshold CMOS

An all-MOS analog implementation of a MAP decoder is presented for the (8, 4) extended Hamming code. This paper describes the design and analysis of a tail-biting trellis decoder implementation using subthreshold CMOS devices. A VLSI test chip has recently returned from fabrication, and preliminary test results indicate accurate decoding up to 20 MBit/s.

Verification of Analog/Mixed-Signal Circuits Using Symbolic Methods

This paper presents two symbolic model checking algorithms for the verification of analog/mixed-signal circuits. The first model checker utilizes binary decision diagrams while the second is a bounded model checker that uses a satisfiability modulo theory solver. Both methods have been implemented, and preliminary results are promising.

Analog/mixed-signal circuit verification using models generated from simulation traces

Formal and semi-formal verification of analog/mixed-signal circuits is complicated by the difficulty of obtaining circuit models suitable for analysis. We propose a method to generate a formal model from simulation traces. The resulting model is conservative in that it includes all of the original simulation traces used to generate it plus additional behavior. Information obtained during the model generation process can also be used to refine the simulation and verification process.

Verification of analog and mixed-signal circuits using timed hybrid petri nets

Embedded systems are composed of a heterogeneous collection of digital, analog, and mixed-signal hardware components. This paper presents a method for the verification of systems composed of such a variety of components. This method utilizes a new model, timed hybrid Petri nets (THPN), to model these circuits. In particular, this paper describes an efficient, approximate algorithm to find the reachable states of a THPN model. Using this state space, desired properties specified in ACTL are verified. To demonstrate these methodologies, a few hybrid automata benchmarks, a tunnel diode oscillator, and a phase-locked loop are modeled and analyzed using THPNs.

Verification of Analog/Mixed-Signal Circuits Using Labeled Hybrid Petri Nets

Mixed-signal designs integrate digital and analog circuits which complicates the already difficult verification problem. This paper presents a model, labeled hybrid Petri nets (LHPNs), that is developed to model this heterogeneous set of components. To support formal verification, this paper presents an efficient zone-based state space exploration algorithm for LHPNs. This algorithm uses a process known as warping which allows zones to describe continuous variables changing at variable rates. Finally, this paper describes the application of this algorithm to analog/mixed-signal circuit examples.

The Case for Analog Circuit Verification

The traditional approach to validate analog circuits is to utilize extensive SPICE-level simulations. The main challenge of this approach is knowing when all important corner cases have been simulated. A new alternative is to utilize formal verification techniques. This paper utilizes a simple example to illustrate the potential flaws of a simulation-only based validation methodology and the potential benefits of formal verification of analog circuits.

Bounded model checking of analog and mixed-signal circuits using an SMT solver

This paper presents a bounded model checking algorithm for the verification of analog and mixed-signal (AMS) circuits using a satisfiability modulo theories (SMT) solver. The systems are modeled in VHDL-AMS, a hardware description language for AMS circuits. In this model, system safety properties are specified as assertion statements. The VHDL-AMS description is compiled into labeled hybrid Petri nets (LHPNs) in which analog values are modeled as continuous variables that can change at rates in a bounded range and digital values are modeled using Boolean signals. The verification method begins by transforming the LHPN model into an SMT formula composed of the initial state, the transition relation unrolled for a specified number of iterations, and the complement of the assertion in each set of state variables. When this formula evaluates to true, this indicates a violation of the assertion and an error trace is reported. This method has been implemented and preliminary results are promising.

Verification of timed circuits with failure-directed abstractions

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 analyzed. An algorithm is also shown to examine the abstract 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.

Symbolic Model Checking of Analog/Mixed-Signal Circuits

This paper presents a Boolean based symbolic model checking algorithm for the verification of analog/mixed-signal (AMS) circuits. The systems are modeled in VHDL-AMS, a hardware description language for AMS circuits. The VHDL-AMS description is compiled into labeled hybrid Petri nets (LH-PNs) in which analog values are modeled as continuous variables that can change at rates in a bounded range and digital values are modeled using Boolean signals. System properties are specified as temporal logic formulas using timed CTL (TCTL). The verification proceeds over the structure of the formula and maps separation predicates to Boolean variables. The state space is thus represented as a Boolean function using a binary decision diagram (BDD) and the verification algorithm relies on the efficient use of BDD operations.