Related papers: Algebraic Barriers to Halving Algorithmic Informat…
We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
Goedel Incompleteness Theorem leaves open a way around it, vaguely perceived for a long time but not clearly identified. (Thus, Goedel believed informal arguments can answer any math question.) Closing this loophole does not seem obvious…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
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 analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set $P$ and are asked to identify a linear extension of $P$ using pairwise comparisons. For the standard sorting…
In this study, the effect of bounded quantum memory in a primitive information protocol has been examined using the quantum Kolmogorov complexity as a measure of information. We employed a toy two-party protocol in which Bob by using a…
The even online Kolmogorov complexity of a string $x = x_1 x_2 \cdots x_{n}$ is the minimal length of a program that for all $i\le n/2$, on input $x_1x_3 \cdots x_{2i-1}$ outputs $x_{2i}$. The odd complexity is defined similarly. The sum of…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually…
We present subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points, belonging to three respective sets $A$, $B$, and $C$ of points in the plane, that satisfy a…
For every total recursive time bound $t$, a constant fraction of all compressible (low Kolmogorov complexity) strings is $t$-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of…
We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…
Clustering large spatial databases is an important problem, which tries to find the densely populated regions in a spatial area to be used in data mining, knowledge discovery, or efficient information retrieval. However most algorithms have…
Communicating state machines provide a formal foundation for distributed computation. Unfortunately, they are Turing-complete and, thus, challenging to analyse. In this paper, we classify restrictions on channels which have been proposed to…
We identify the free half shuffle algebra of Sch\"utzenberger (1958) with an algebra of real-valued functionals on paths, where the half shuffle emulates integration of a functional against another. We then provide two, to our knowledge,…
Communicating state machines provide a formal foundation for distributed computation. Unfortunately, they are Turing-complete and, thus, challenging to analyse. In this paper, we classify restrictions on channels which have been proposed to…
The (prefix-free) Kolmogorov complexity of a finite binary string is the length of the shortest description of the string. This gives rise to some `standard' lowness notions for reals: A is K-trivial if its initial segments have the lowest…