相关论文: Cypher is Turing-Complete: A Formal Proof via 2-Co…

An efficient technique of computing on encrypted data allows a client with limited capability to perform complex operations on a remote fault-tolerant server without leaking anything about the input or output. Quantum computing provides…

Quantum money is the cryptographic application of the quantum no-cloning theorem. It has recently been instantiated by Montgomery and Sharif (Asiacrypt '24) from class group actions on elliptic curves. In this work, we propose a concrete…

We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…

We show that any language in nondeterministic time $\exp(\exp(\cdots \exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical…

Explaining why an answer is (or is not) returned by a query is important for many applications including auditing, debugging data and queries, and answering hypothetical questions about data. In this work, we present the first practical…

We prove that Balanced Biclique Reconfiguration on bipartite graphs is PSPACE-complete. This implies the PSPACE-completeness of the spanning variant of Subgraph Reconfiguration under the token jumping rule for the property "a graph is an…

We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal), motivated by recent advances in near-term quantum computing hardware and the related embedding problems. We assemble a preprocessing…

Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…

For all $k \geq 1$, we show that deciding whether a graph is $k$-planar is NP-complete, extending the well-known fact that deciding 1-planarity is NP-complete. Furthermore, we show that the gap version of this decision problem is…

Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded…

A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…

Reed showed that, if two graphs are $P_4$-isomorphic, then either both are perfect or none of them is. In this note we will derive an analogous result for perfect digraphs.

It is well known that kernels in graphs are powerful and useful structures, for instance in the theory of games. However, a kernel does not always exist and Chv\'atal proved in 1973 that it is an NP-Complete problem to decide its existence.…

Quantum states obey an asymptotic no-cloning theorem, stating that no deterministic machine can reliably replicate generic sequences of identically prepared pure states. In stark contrast, we show that generic sequences of unitary gates can…

In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows…

We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in…

This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of…

We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them. Those grammars can alternatively be viewed as an…

Interaction between clique number $\omega(G) $ and chromatic number $\chi(G) $ of a graph is a well studied topic in graph theory. Perfect Graph Theorems are probably the most important results in this direction. Graph $G$ is called…

We study the question of what is computable by Turing machines equipped with time travel into the past; i.e., with Deutschian closed timelike curves (CTCs) having no bound on their width or length. An alternative viewpoint is that we study…