Related papers: A Hierarchy for Constant Communication Complexity
We consider the complexity (in terms of the arithmetical hierarchy) of the various quantifier levels of the diagram of a computably presented metric structure. As the truth value of a sentence of continuous logic may be any real in $[0,1]$,…
Quantum systems generally exhibit different kinds of correlations. In order to compare them on equal footing, one uses the so-called distance-based approach where different types of correlations are captured by the distance to different…
This paper is the extended version of On the Complexity of Infinite Advice Strings (ICALP 2018). We investigate a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a…
We say that two classes of topological spaces are equivalent if each member of one class has a homeomorphic copy in the other class and vice versa. Usually when the Borel complexity of a class of metrizable compacta is considered, the class…
We extend the definitions of complexity measures of functions to domains such as the symmetric group. The complexity measures we consider include degree, approximate degree, decision tree complexity, sensitivity, block sensitivity, and a…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
Motivated by the quest for a broader understanding of communication complexity of simple functions, we introduce the class of "permutation-invariant" functions. A partial function $f:\{0,1\}^n \times \{0,1\}^n\to \{0,1,?\}$ is…
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the…
We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…
Several performance measures can be used for evaluating classification results: accuracy, F-measure, and many others. Can we say that some of them are better than others, or, ideally, choose one measure that is best in all situations? To…
We introduce a restriction of the classical 2-party deterministic communication protocol where Alice and Bob are restricted to using only comparison functions. We show that the complexity of a function in the model is, up to a constant…
Communication complexity is the amount of communication needed to compute a function when the function inputs are distributed over multiple parties. In its simplest form, one-way communication complexity, Alice and Bob compute a function…
An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a…
We investigate the question which communication tasks can be accomplished within a given operational theory. The concrete task is to find out which communication matrices have a prepare-and-measure implementation with states and measurement…
We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities…
In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy,…
Communication complexity is a fundamental aspect of information science, concerned with the amount of communication required to solve a problem distributed among multiple parties. The standard quantification of one-way communication…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…