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A Faithful Semantics for Generalised Symbolic Trajectory Evaluation
Generalised Symbolic Trajectory Evaluation (GSTE) is a high-capacity formal
verification technique for hardware. GSTE uses abstraction, meaning that
details of the circuit behaviour are removed from the circuit model. A
semantics for GSTE can be used to predict and understand why certain circuit
properties can or cannot be proven by GSTE. Several semantics have been
described for GSTE. These semantics, however, are not faithful to the proving
power of GSTE-algorithms, that is, the GSTE-algorithms are incomplete with
respect to the semantics.
The abstraction used in GSTE makes it hard to understand why a specific
property can, or cannot, be proven by GSTE. The semantics mentioned above
cannot help the user in doing so. The contribution of this paper is a faithful
semantics for GSTE. That is, we give a simple formal theory that deems a
property to be true if-and-only-if the property can be proven by a GSTE-model
checker. We prove that the GSTE algorithm is sound and complete with respect to
this semantics
Lower Bounds for Monotone Counting Circuits
A {+,x}-circuit counts a given multivariate polynomial f, if its values on
0-1 inputs are the same as those of f; on other inputs the circuit may output
arbitrary values. Such a circuit counts the number of monomials of f evaluated
to 1 by a given 0-1 input vector (with multiplicities given by their
coefficients). A circuit decides if it has the same 0-1 roots as f. We
first show that some multilinear polynomials can be exponentially easier to
count than to compute them, and can be exponentially easier to decide than to
count them. Then we give general lower bounds on the size of counting circuits.Comment: 20 page
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