Related papers: Cypher is Turing-Complete: A Formal Proof via 2-Co…
This paper addresses the following verification task: Given a graph transformation system and a class of initial graphs, can we guarantee (non-)reachability of a given other class of graphs that characterizes bad or erroneous states? Both…
A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $(x,y)\in E$. Halld\'{o}rsson et al.\ have shown that a graph is…
We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a…
We study constraint satisfaction problems (CSPs) in the presence of counting quantifiers $\exists^{\geq j}$, asserting the existence of $j$ distinct witnesses for the variable in question. As a continuation of our previous (CSR 2012) paper,…
The quantum circuit model is the default for encoding an algorithm intended for a NISQ computer or a quantum computing simulator. A simple graph and through it, a graph state - quantum state physically manifesting an abstract graph…
We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient…
Parsing is an important problem in computer science and yet surprisingly little attention has been devoted to its formal verification. In this paper, we present TRX: a parser interpreter formally developed in the proof assistant Coq,…
We demonstrate that when a graph exhibits a specific type of symmetry, it satisfies the Union Closed Conjecture(UCC). Additionally, we show that certain graph classes, such as Cylindrical Grid Graphs and Torus Grid Graphs also satisfy the…
In this paper we present the formal, computer-supported verification of a functional implementation of Buchberger's critical-pair/completion algorithm for computing Gr\"obner bases in reduction rings. We describe how the algorithm can be…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
A graph $G$ is said to be a `set graph' if it admits an acyclic orientation that is also `extensional', in the sense that the out-neighborhoods of its vertices are pairwise distinct. Equivalently, a set graph is the underlying graph of the…
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates…
In this paper we present a new "external checker" for the Lean theorem prover, written in Lean itself. This is the first complete typechecker for Lean 4 other than the reference implementation in C++ used by Lean itself, and our new checker…
This article presents the application of homomorphic authenticators, replication encodings to be precise, to multigroup fully homomorphic encryption schemes. Following the works of Gennaro and Wichs on homomorphic authenticators in…
CompCert is the first realistic formally verified compiler: it provides a machine-checked mathematical proof that the code it generates matches the source code. Yet, there could be loopholes in this approach. We comprehensively analyze…
Recursive techniques have recently been introduced into quantum programming so that a variety of large quantum circuits and algorithms can be elegantly and economically programmed. In this paper, we present a proof system for formal…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…
ZX-calculus is a graphical language for quantum computing which is complete in the sense that calculation in matrices can be done in a purely diagrammatic way. However, all previous universally complete axiomatisations of ZX-calculus have…