Related papers: State complexity of catenation combined with boole…
We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to…
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…
We consider a large coupling limit of a Born-Infeld action in a curved background of an arbitrary metric and a constant two form field. Following hep-th/0009061, we go to the Hamiltonian description. The Hamiltonian can be dualized and the…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
It is shown that a large class of properties coincide for weighted composition operators on a large class of weighted VMOA spaces, including the ones with logarithmic weights and the ones with standard weights $(1-|z|)^{-c}, \ 0\leq c<…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
In this paper, we consider the transition complexity of regular languages based on the incomplete deterministic finite automata. A number of results on Boolean operations have been obtained. It is shown that the transition complexity…
The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…
Compositional Explanations is a method for identifying logical formulas of concepts that approximate the neurons' behavior. However, these explanations are linked to the small spectrum of neuron activations (i.e., the highest ones) used to…
We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is…
We present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of Cohen strongly summing linear operators. Our argument is extended to multilinear operators and, as a consequence, we…
We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…
We investigate the class of bisymmetric and quasitrivial binary operations on a given set $X$ and provide various characterizations of this class as well as the subclass of bisymmetric, quasitrivial, and order-preserving binary operations.…
We study classes of objects whose combinatorics are closely related to those of posets. The framework of operads and operad algebras allows us to make this relationship precise and provides tools for a deeper understanding of their…
We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is…
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…