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Learning binary representations of instances and classes is a classical problem with several high potential applications. In modern settings, the compression of high-dimensional neural representations to low-dimensional binary codes is a…
Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…
We present an algorithm to solve the Simultaneous Unitary Similarity(S.U.S) problem which is to check if there exists a Similarity transformation determined by a Unitary $U$ s.t $UA_lU^*=B_l$, $l \in \{1,...,p\}$, where $A_l$ and $B_l$ are…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
First of all we give some reasons that "natural proofs" built not a barrier to prove P $\not=$ NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the…
Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks,…
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
We study the problem of agnostic learning under the Gaussian distribution. We develop a method for finding hard families of examples for a wide class of problems by using LP duality. For Boolean-valued concept classes, we show that the…
We study the classification problems over string data for hypotheses specified by formulas of monadic second-order logic MSO. The goal is to design learning algorithms that run in time polynomial in the size of the training set,…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…
We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in n^(lg^2 n) time. Further, our algorithm is oblivious to the order of the variables. This is…
A Qualitative Constraint Network (QCN) is a constraint graph for representing problems under qualitative temporal and spatial relations, among others. More formally, a QCN includes a set of entities, and a list of qualitative constraints…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a…
In recent work, we have introduced a framework for fine-grained consent management in databases, which combines Boolean data provenance with the field of interactive Boolean evaluation. In turn, interactive Boolean evaluation aims at…
In this paper we study the approximate learnability of valuations commonly used throughout economics and game theory for the quantitative encoding of agent preferences. We provide upper and lower bounds regarding the learnability of…