Related papers: Polynomial Circuit Verification using BDDs
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…
Deciding in an efficient way weak probabilistic bisimulation in the context of Probabilistic Automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the…
Formal verification has been successfully developed in computer science for verifying combinatorial classes of models and specifications. In like manner, formal verification methods have been developed for dynamical systems. However, the…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study…
It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-commutative one-dimensional and to have two connected…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
The obvious way to construct a GDD (group-divisible design) recursively is to use Wilson's Fundamental Construction for GDDs (WFC). Then a PBD (pairwise balanced design) is often obtained by adding a new point to each group of the GDD.…
The use of neural networks as function approximators has enabled many advances in reinforcement learning (RL). The generalization power of neural networks combined with advances in RL algorithms has reignited the field of artificial…
We suggest a purely combinatorial approach to a general problem in system reliability. We show how to determine if a given vector can be the signature of a system, and in the affirmative case exhibit such a system in terms on its structure…
We prove that checking if a partial matrix is partial totally positive is co-NP-complete. This contrasts with checking a conventional matrix for total positivity, for which we provide a cubic time algorithm. Checking partial sign regularity…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
The P versus NP problem asks whether every language verifiable in polynomial time can also be decided in deterministic polynomial time. In this paper, we present a constructive proof that P = NP by introducing a universal, graph-based…
In this thesis a comprehensive verification framework is proposed to contend with some important issues in composability verification and a verification process is suggested to verify composability of different kinds of systems models, such…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
It is already shown that a Boolean function for a NP-complete problem can be computed by a polynomial-sized circuit if its variables have enough number of automorphisms. Looking at this previous study from the different perspective gives us…
An algebraic group ring method for constructing codes with no short cycles in the check matrix is derived. It is shown that the matrix of a group ring element has no short cycles if and only if the collection of group differences of this…
This paper introduces a novel method for synthesizing digital circuits derived from Binary Decision Diagrams (BDDs) that can yield to reduction in power dissipation. The power reduction is achieved by decreasing the switching activity in a…
We construct validation designs $Z_m$ aimed at estimating the integrated squared prediction error of a given design $X_n$. Our approach is based on the minimization of a maximum mean discrepancy for a particular kernel, conditional on…
The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for obstructions to the nerve lemma, statistical considerations of multiple testing quickly…