Related papers: A Finitely presented group whose word problem has …
Committee selection with diversity or distributional constraints is a ubiquitous problem. However, many of the formal approaches proposed so far have certain drawbacks including (1) computationally intractability in general, and (2)…
We study the computational complexity of some explainable clustering problems in the framework proposed by [Dasgupta et al., ICML 2020], where explainability is achieved via axis-aligned decision trees. We consider the $k$-means,…
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
A graph class is hereditary if it is closed under vertex deletion. We give examples of NP-hard, PSPACE-complete and NEXPTIME-complete problems that become constant-time solvable for every hereditary graph class that is not equal to the…
We prove new complexity results for computational problems in certain wreath products of groups and (as an application) for free solvable group. For a finitely generated group we study the so-called power word problem (does a given…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
We show that for any finite group $G$ and for any $d$ there exists a word $w\in F_{d}$ such that a $d$-tuple in $G$ satisfies $w$ if and only if it generates a solvable subgroup. In particular, if $G$ itself is not solvable, then it cannot…
An object--oriented approach to create a natural language understanding system is considered. The understanding program is a formal system built on the base of predicative calculus. Horn's clauses are used as well--formed formulas. An…
I present an analytic approach to establishing the presence of phase transitions in a large set of decision problems. This approach does not require extensive computational study of the problems considered. The set -- that of all paddable…
An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the…
*by a standard (one-tape) Turing machine. It is well-known that the word problem for hyperbolic groups, whence in particular for free groups, can be solved in linear time. However, these algorithms run on machines more complicated than a…
We study the problem of finding a subgroup of a given order in a finite group, where the group is represented by its Cayley table. We analyze the complexity of the problem in the special case of abelian groups and present an optimal…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
We explore the effect of finite population sampling in design problems with many variables cross-classified in many ways. In particular, we investigate designs where we wish to sample individuals belonging to different groups for which the…
We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…
We propose a new method of classifying documents into categories. The simple method of conducting hypothesis testing over word-based distributions in categories suffers from the data sparseness problem. In order to address this difficulty,…
We give a ranker-based description using finite-index congruences for the variety $\boldsymbol{\mathrm{DAb}}$ of finite monoids whose regular $\mathcal{D}$-classes form Abelian groups. This combinatorial description yields a normal form for…
The complexity of a computational problem is traditionally quantified based on the hardness of its worst case. This approach has many advantages and has led to a deep and beautiful theory. However, from the practical perspective, this…
In the paper we characterize the class of finite solvable groups by two-variable identities in a way similar to the characterization of finite nilpotent groups by Engel identities. More precisely, a sequence of words $u_1,...,u_n,... $ is…