Related papers: Polynomial Circuit Verification using BDDs
We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete for subclasses of the counting…
Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs…
Polynomial Networks (PNs) have demonstrated promising performance on face and image recognition recently. However, robustness of PNs is unclear and thus obtaining certificates becomes imperative for enabling their adoption in real-world…
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Understanding how neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying circuits - minimal subnetworks responsible for specific…
Polymorphic circuits are a special kind of digital logic components, which possess multiple build-in functions. In different environments, a polymorphic circuit would perform different functions. Evolutionary Algorithms, Binary Decision…
The question how to certify non-negativity of a polynomial function lies at the heart of Real Algebra and also has important applications to Optimization. In this article we investigate the question of non-negativity in the context of…
Formal software verification techniques are widely used to specify and prove the functional correctness of programs. However, nonfunctional properties such as time complexity are usually carried out with pen and paper. Inefficient code in…
We show that the GCD of two univariate polynomials can be computed by (piece-wise) algebraic circuits of constant depth and polynomial size over any sufficiently large field, regardless of the characteristic. This extends a recent result of…
In this talk, we will describe a framework for assertion-based verification (ABV) of quantum circuits by applying model checking techniques for quantum systems developed in our previous work, in which: (i) Noiseless and noisy quantum…
It is proved that any polynomial vector field in two complex variables which is complete on a non-algebraic trajectory is complete.
As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in…
This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and…
Software methods introduced for automated design of approximate implementations of arithmetic circuits rely on fast and accurate evaluation of approximate candidate implementations. To accelerate the evaluation of circuit error, we propose…
Hyperproperties are system properties that require quantification over multiple execution traces of a system. Hyperproperties can express several specifications of interest for cyber-physical systems--such as opacity, robustness, and…
We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with $n$ nodes can be drawn on a $\sqrt n$ by $\sqrt n$ grid. We also show that testing whether a given binary tree has…
Probabilistic circuits (PCs) are a unifying representation for probabilistic models that support tractable inference. Numerous applications of PCs like controllable text generation depend on the ability to efficiently multiply two circuits.…
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…
Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates…