计算复杂性

We study the structural expressivity and the parameterised complexity of counting homomorphisms from small temporal patterns to large temporal graphs. Here, a temporal pattern $P$ consists of a graph together with a partial order on its…

We prove that the minimum edge-outerplanarity of a planar graph can be computed in polynomial time, resolving an open problem of Bentz (2009). The proof was initially produced by GPT~5.5 Pro and then verified and polished manually.

We prove an information-theoretically optimal \emph{gap-majority lemma} in the two-player randomized communication model. For a base function $f: \mathcal{X} \to \{\pm 1\}$, its $n$-fold \emph{gap-majority composition}, denoted…

We introduce an activation hierarchy consisting of stage machines, stage domains, and stage languages generated by an activation operator. The central result is a Predictor-Impossibility Theorem (PIT), which shows that no effective…

The Stochastic-Oracle Turing Machine (SOTM) framework models AI-augmented computation as the interaction of a probabilistic Turing machine with an oracle whose responses are drawn from context-dependent distributions. This paper studies…

The parameterized Minimum Monotone Satisfying Assignment ($k$-MMSA) problem asks whether a monotone Boolean circuit admits a satisfying assignment of Hamming weight at most $k$. The MMSA hierarchy is defined by allowing a bounded number of…

G.\ D.\ Baker formulated a forcing method to interpret integer optimisation problem into $2$-adic linear regression, and proved the NP-hardness of $2$-adic linear regression. We generalise the forcing method to a wider class of $p$-adic…

We prove an $\tilde{\Omega}(n^2)$ lower bound for read-once parity branching programs computing an explicit boolean function on $n$ variables. The previous best lower bound was $\tilde{\Omega}(n^{1.5})$. Our lower bound is proved by…

Introduced by Lee, Ko, and Shin (VLDB 2020), a hypergraph motif is a connected subhypergraph consisting of three hyperedges whose intersections satisfy a prescribed pattern. Such patterns are represented by Venn diagrams…

Given a nonnegative matrix $X$, a factorization rank $r$ and a real parameter $p$, entrywise power matrix factorization (EPMF) looks for a low-rank matrix $X_r$ such that $X = |X_r|^{\circ p}$ (exact case) or $X \approx |X_r|^{\circ p}$…

We introduce the subcube stifling number, a new combinatorial measure of total Boolean functions. This measure is the largest integer $k$ such that, for every set $S$ of at most $k$ input variables and every assignment $b \in \{0,1\}^S$,…

We study Boolean functions and their Fourier spectrum supports in the context of parity decision trees (PDTs). Recently, H.~Hatami et al.~\cite{HHL+} constructed examples whose Fourier support \(\mathcal S\) satisfies $$ |(\mathcal…

We study some properties of the parity based bit-counting complexity classes ${\bf B_{|0| \oplus}P}$ and ${\bf B_{|1| \oplus}P}$. We first show that both of these complexity classes are closed under complement and prove that ${\bf…

Strassen's theory of bilinear complexity provides a mathematical characterization of the arithmetic complexity of primitives such as matrix multiplication via the rank of tensors. However, the connection to tensor rank is known to break…

Self-reference and solution independence are core properties underlying intractability. This paper establishes a finite combinatorial analogue of G\"odel's incompleteness theorems within Boolean $K$-SAT. While standard random $K$-SAT has…

While the Church-Turing thesis asserts that effective calculability explicates to sets decidable by a Turing machine, the Cobham-Edmonds thesis asserts that feasible computation explicates to the complexity class $\mathsf{P}$, those…

For every $\varepsilon > 0$, Max Independent Set admits a polynomial-time $n^\varepsilon$-approximation algorithm on $n$-vertex graphs of effectively bounded twin-width [Berg\'e et al., STACS '23]. The approximation factor actually obtained…

Jerrum and Meeks (TOCT, JCSS 2015) introduced the counting problems $\text{IndSub}(\Phi)$ for fixed graph properties $\Phi$: Given an input graph $G$ and $k\in\mathbb N$, count the $k$-vertex subsets $S \subseteq V(G)$ such that the induced…

Time complexity typically assumes $O(1)$ cost per data access. This paper presents an analysis based on an abstract memory hierarchy. For a common class of applications, it shows that the data-access cost scales with the fourth root of data…

Boolean networks are finite discrete nonlinear systems whose long-term behaviour is organised by fixed-point and cyclic attractors. Detecting such recurrent states is important in applications ranging from gene regulation and neural…