Related papers: Nondeterministic Communication Complexity of Rando…
We study the expressivity and the complexity of various logics in probabilistic team semantics with the Boolean negation. In particular, we study the extension of probabilistic independence logic with the Boolean negation, and a recently…
We formulate a model for intermittent communication that can capture bursty transmissions or a sporadically available channel, where in either case the receiver does not know a priori when the transmissions will occur. Focusing on the…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
Communication games are crucial tools for investigating the limitations of physical theories. The communication complexity (CC) problem is a typical example, for which several distributed parties attempt to jointly calculate a given…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
This paper describes a purely functional library for computing level-$p$-complexity of Boolean functions, and applies it to two-level iterated majority. Boolean functions are simply functions from $n$ bits to one bit, and they can describe…
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed…
It is shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with high probability, the configuration with an arbitrary small percent of random errors gives almost no prediction…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
In this paper, we consider classes of decision tables with many-valued decisions closed under operations of removal of columns, changing of decisions, permutation of columns, and duplication of columns. We study relationships among three…
We consider a problem of decomposition of a ternary function into a composition of binary ones from the viewpoint of communication complexity and algorithmic information theory as well as some applications to cellular automata.
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
In this work we cast the problem of binary classification in terms of estimating a partition on Bernoulli data. When the explanatory variables are all categorical, the problem can be modelled using the language of boolean functions. We…
We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently…
In this short note, we initiate the study of the Linear Isomorphism Testing Problem in the setting of communication complexity, a natural linear algebraic generalization of the classical Equality problem. Given Boolean functions $f, g :…
In this paper, we study the query complexity of Boolean functions in the presence of uncertainty, motivated by parallel computation with an unlimited number of processors where inputs are allowed to be unknown. We allow each query to…
We study the complexity of basic regular operations on languages represented by incomplete deterministic or nondeterministic automata, in which all states are final. Such languages are known to be prefix-closed. We get tight bounds on both…
We show that any bounded integral function $f : A \times B \mapsto \{0,1, \dots, \Delta\}$ with rank $r$ has deterministic communication complexity $\Delta^{O(\Delta)} \cdot \sqrt{r} \cdot \log r$, where the rank of $f$ is defined to be the…