Related papers: Verifying Time Complexity of Deterministic Turing …

Runtime Verification deals with the question of whether a run of a system adheres to its specification. This paper studies runtime verification in the presence of partial knowledge about the observed run, particularly where input values may…

The NP-complete Permutation Pattern Matching problem asks whether a $k$-permutation $P$ is contained in a $n$-permutation $T$ as a pattern. This is the case if there exists an order-preserving embedding of $P$ into $T$. In this paper, we…

The Busy Beaver Challenge (or bbchallenge) aims at collaboratively solving the following conjecture: "$S(5) = 47{,}176{,}870$" [Rad\'o, 1962], [Marxen and Buntrock, 1990], [Aaronson, 2020]. This conjecture says that if a 5-state Turing…

Working in the multitape Turing model, we show how to reduce the problem of matrix transposition to the problem of integer multiplication. If transposing an $n \times n$ binary matrix requires $\Omega(n^2 \log n)$ steps on a Turing machine,…

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…

The deterministic membership problem for timed automata asks whether the timed language given by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. An analogous problem can be stated in the setting of…

We show conditional lower bounds for well-studied #P-hard problems: (a) The number of satisfying assignments of a 2-CNF formula with n variables cannot be counted in time exp(o(n)), and the same is true for computing the number of all…

We consider the model checking problem of infinite state systems given in the form of parameterized discrete timed networks with multiple clocks. We show that this problem is decidable with respect to specifications given by B- or…

In this paper we study algorithms for tiling problems. We show that the conditions $(T1)$ and $(T2)$ of Coven and Meyerowitz, conjectured to be necessary and sufficient for a finite set $A$ to tile the integers, can be checked in time…

Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…

Opacity is a property of privacy and security applications asking whether, given a system model, a passive intruder that makes online observations of system's behaviour can ascertain some "secret" information of the system. Deciding opacity…

Given a machine $U$, a $c$-short program for $x$ is a string $p$ such that $U(p)=x$ and the length of $p$ is bounded by $c$ + (the length of a shortest program for $x$). We show that for any standard Turing machine, it is possible to…

Timed automata are a widely used formalism for specifying the discrete-state/continuous-time behavior of time-critical reactive systems. For the fundamental verification problem of comparing two timed automata, it has been shown that timed…

We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…

This paper investigates the decidability of opacity in timed automata (TA), a property that has been proven to be undecidable in general. First, we address a theoretical gap in recent work by J. An et al. (FM 2024) by providing necessary…

The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many…

*by a standard (one-tape) Turing machine. It is well-known that the word problem for hyperbolic groups, whence in particular for free groups, can be solved in linear time. However, these algorithms run on machines more complicated than a…

We show, assuming the (randomized) Gap Exponential Time Hypothesis (Gap-ETH), that the following tasks cannot be done in $T(k) \cdot N^{o(k)}$-time for any function $T$ where $N$ denote the input size: - $\left(1 - \frac{1}{e} +…

We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…

Given an undirected graph G = (V, E) with n vertices, and a function f : V -> N, we consider the problem of finding a connected f -factor in G. In this work we design an algorithm to check for the existence of a connected f -factor, for the…