ACM Transactions on Computation Theory

Constraint satisfaction problems (CSP) encompass an enormous variety of computational problems. In particular, all partition functions from statistical physics, such as spin systems, are special cases of counting CSP (#CSP). We prove a complete complexity ...

We prove the first genuine quantified Boolean formula (QBF) proof size lower bounds for the proof system Merge Resolution (MRes), a refutational proof system for prenex QBFs with a CNF matrix. Unlike most QBF resolution systems in the literature, proofs ...

We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification of undirected graphs. Given a weighted, undirected graph G on n vertices described by a binary string of length N, an integer k ≤ log n, and an error parameter ɛ >...

We revisit recent developments for the Maximum Weight Independent Set problem in graphs excluding a subdivided claw S_t,t,t as an induced subgraph and provide a subexponential-time algorithm with improved running time \(\(2^{\mathcal {O}(\sqrt {nt}\log n)}\)...\)

We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows: Let \(\(f : \mathbb ...\)

Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to obtain polynomial-...

Discrete dynamical systems serve as useful formal models to study diffusion phenomena in social networks. Several recent articles have studied the algorithmic and complexity aspects of some decision problems on synchronous Boolean networks, which are ...

In this work, we consider d-Hyperedge Estimation and d-Hyperedge Sample problems that deal with estimation and uniform sampling of hyperedges in a hypergraph ℋ(U(ℋ), ℱ(ℋ) in the query complexity framework, where U(ℋ) denotes the set of vertices and ℱ(ℋ) ...