计算复杂性
By a tight tour in a $k$-uniform hypergraph $H$ we mean any sequence of its vertices $(w_0,w_1,\ldots,w_{s-1})$ such that for all $i=0,\ldots,s-1$ the set $e_i=\{w_i,w_{i+1}\ldots,w_{i+k-1}\}$ is an edge of $H$ (where operations on indices…
Given a graph $F$, let $I(F)$ be the class of graphs containing $F$ as an induced subgraph. Let $W[F]$ denote the minimum $k$ such that $I(F)$ is definable in $k$-variable first-order logic. The recognition problem of $I(F)$, known as…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In…
In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling…
Characterising tractable fragments of the constraint satisfaction problem (CSP) is an important challenge in theoretical computer science and artificial intelligence. Forbidding patterns (generic sub-instances) provides a means of defining…
We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of O(1)-deepK, O(1)-deepC , order-deep K and order-deep C sequences. Our main results are that Martin-Loef random sets are not…
We show that if $\mathbb A$ is a core relational structure such that CSP($\mathbb A$) can be solved by a linear Datalog program, and $\mathbb A$ is $n$-permutable for some $n$, then CSP($\mathbb A$) can be solved by a symmetric Datalog…
Given a Boolean formula $\phi$ over $n$ variables, the problem of model counting is to compute the number of solutions of $\phi$. Model counting is a fundamental problem in computer science with wide-ranging applications. Owing to the…
The topology-aware Massively Parallel Computation (MPC) model is proposed and studied recently, which enhances the classical MPC model by the awareness of network topology. The work of Hu et al. on topology-aware MPC model considers only…
We define a new, partizan, loopy combinatorial game, Forced-Capture Hnefatafl, similar to Hnefatafl, except that players are forced to make capturing moves when available. We show that this game is PSPACE-hard using a reduction from…
Minimizing the weight of an edge set satisfying parity constraints is a challenging branch of combinatorial optimization as witnessed by the binary hypergraph chapter of Alexander Schrijver's book ``Combinatorial Optimization" (Chapter 80).…
In this paper, we present a much simpler, direct and elegant approach to the equivalence problem of {\it measure many one-way quantum finite automata} (MM-1QFAs). The approach is essentially generalized from the work of Carlyle [J. Math.…
In this paper we consider the weighted $k$-Hamming and $k$-Edit distances, that are natural generalizations of the classical Hamming and Edit distances. As main results of this paper we prove that for any $k\geq 2$ the DECIS-$k$-Hamming…
A vertex $w$ resolves two vertices $u$ and $v$ in a directed graph $G$ if the distance from $w$ to $u$ is different to the distance from $w$ to $v$. A set of vertices $R$ is a resolving set for a directed graph $G$ if for every pair of…
We show that the sum of a sequence of integers can be computed in linear time on a Turing machine. In particular, the most obvious algorithm for this problem, which appears to require quadratic time due to carry propagation, actually runs…
This paper describes the formal verification of NP-hardness reduction functions of two key problems relevant in algebraic lattice theory: the closest vector problem and the shortest vector problem, both in the infinity norm. The…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
In this paper we investigate formal verification problems for Neural Network computations. Various reachability problems will be in the focus, such as: Given symbolic specifications of allowed inputs and outputs in form of Linear…
We consider a classical envy-free cake cutting problem. The first limited protocol was proposed by Aziz and McKenzie in 2016 arXiv:1604.03655. The disadvantage of this protocol is its high complexity. The authors proved that the maximum…