Formal property verification by abstraction refinement with formal, simulation and hybrid engines
We present RFN, a formal property verification tool based on abstraction refinement. Abstraction refinement is a strategy for property verification. It iteratively refines an abstract model to better approximate the behavior of the original design in the hope that the abstract model alone will provide enough evidence to prove or disprove the property. However, previous work on abstraction refinement was only demonstrated on designs with up to 500 registers. We developed RFN to verify real-world designs that may contain thousands of registers. RFN differs from the previous work in several ways. First, instead of relying on a single engine, RFN employs multiple formal verification engines, including a BDD-ATPG hybrid engine and a conventional BDD-based fixpoint engine, for finding error traces or proving properties on the abstract model. Second, RFN uses a novel two-phase process involving 3-valued simulation and sequential ATPG to determine how to refine the abstract model. Third, RFN avoids the weakness of other abstraction-refinement algorithms-finding error traces on the original design, by utilizing the error trace of the abstract model to guide sequential ATPG to find an error trace on the original design. We implemented and applied a prototype of RFN to verify various properties of real-world RTL designs containing approximately 5,000 registers, which represents an order of magnitude improvement over previous results. On these designs, we successfully proved a few properties and discovered a design violation.

title: Automated Abstraction Refinement for Model Checking Large State Spaces Using SAT Based Conflict Analysis
abstract: We introduce a SAT based automatic abstraction refinement framework for model checking systems with several thousand state variables in the cone of influence of the specification. The abstract model is constructed by designating a large number of state variables as invisible. In contrast to previous work where invisible variables were treated as free inputs we describe a computationally more advantageous approach in which the abstract transition relation is approximated by pre-quantifying invisible variables during image computation. The abstract counterexamples obtained from model-checking the abstract model are symbolically simulated on the concrete system using a state-of-the-art SAT checker. If no concrete counterexample is found, a subset of the invisible variables is reintroduced into the system and the process is repeated. The main contribution of this paper are two new algorithms for identifying the relevant variables to be reintroduced. These algorithms monitor the SAT checking phase in order to analyze the impact of individual variables. Our method is complete for safety properties (AGp) in the sense that - performance permitting - a property is either verified or disproved by a concrete counterexample. Experimental results are given to demonstrate the power of our method on real-world designs.

title: Stability analysis of biological systems with real solution classification
abstract: This paper presents a new and general approach for analyzing the stability of a large class of biological networks, modeled as autonomous systems of differential equations, using real solving and solution classification. The proposed approach, based on the classical technique of linearization from the qualitative theory of ordinary differential equations yet with exact symbolic computation, is applied to analyzing the local stability of the Cdc2-cyclin B/Wee1 system and the Mos/MEK/p42 MAPK cascade, two well-known models for cell and protein signaling that have been studied extensively in the literature. We provide rigorous proofs and generalizations for some of the previous results established experimentally and report our new findings.

title: On Wu's Method for Proving Constructive Geometric Theorems
abstract: In 1977 Wu Wen-tsiin discovered an efficient method for mechanical theorem proving. This method has been applied to prove and discover theorems in various kinds of geometries. Based on an extension of one of Wu's algorithmic procedures, the author implemented a prover CPS for proving so-called constructive geometric theorems, as well as a general theorem prover PS. Using this prover we proved more than one hundred non-trivial theorems and discovered also a number of interesting ones. This paper is a summarization of our early work, as a abbreviation of the chapter 2 from my Chinese doctoral dissertation.

title: Polynomial Systems from Certain Differential Equations
abstract: In this paper, combined elimination techniques are applied to establish relations among center conditions for certain cubic differential systems initially investigated by Kukles in 1944. The obtained relations clarify recent rediscoveries of some known conditions of Cherkas. The computational difficulties of establishing the complete center conditions for Kukles? system, a problem that is still open, are illustrated by interactive elimination. Some generated polynomial systems that need be solved are made available electronically for other developers to test elimination algorithms and their implementations.

title: On Connectedness: A Solution Based on Oscillatory Correlation
abstract: A long-standing problem in neural computation has been the problem of connectedness, first identified by Minsky and Papert (1969). This problem served as the cornerstone for them to establish analytically that perceptrons are fundamentally limited in computing geometrical (topological) properties. A solution to this problem is offered by a different class of neural networks: oscillator networks. To solve the problem, the representation of oscillatory correlation is employed, whereby one pattern is represented as a synchronized block of oscillators and different patterns are represented by distinct blocks that desynchronize from each other. Oscillatory correlation emerges from LEGION (locally excitatory globally inhibitory oscillator network), whose architecture consists of local excitation and global inhibition among neural oscillators. It is further shown that these oscillator networks exhibit sensitivity to topological structure, which may lay a neurocomputational foundation for explaining the psychophysical phenomenon of topological perception.

title: A schema-based model for phonemic restoration
abstract: Phonemic restoration is the perceptual synthesis of phonemes when masked by appropriate replacement sounds by utilizing linguistic context. Current models attempting to accomplish acoustic restoration of phonemes, however, use only temporal continuity and produce poor restoration of unvoiced phonemes, and are also limited in their ability to restore voiced phonemes. We present a schema-based model for phonemic restoration. The model employs a missing data speech recognition system to decode speech based on intact portions and activates word templates corresponding to the words containing the masked phonemes. An activated template is dynamically time warped to the noisy word and is then used to restore the speech frames corresponding to the masked phoneme, thereby synthesizing it. The model is able to restore both voiced and unvoiced phonemes with a high degree of naturalness. Systematic testing shows that this model outperforms a Kalman-filter based model.