Related papers: Unconventional complexity classes in unconventiona…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected…
Tangle machines are topologically inspired diagrammatic models. Their novel feature is their natural notion of equivalence. Equivalent tangle machines may differ locally, but globally they are considered to share the same information…
Nonuniform families of polynomial-size finite automata, which are series of indexed finite automata having polynomially many inner states, are used in the past literature to solve nonuniform families of promise decision problems. Among such…
Sometimes, mathematical oddities crowd in upon one another, and the exceptions to one classification scheme reveal themselves as fellow-travelers with the exceptions to a quite different taxonomy.
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…
One-counter processes (OCPs) are pushdown processes which operate only on a unary stack alphabet. We study the computational complexity of model checking computation tree logic (CTL) over OCPs. A PSPACE upper bound is inherited from the…
We study the bisimilarity problem for probabilistic pushdown automata (pPDA) and subclasses thereof. Our definition of pPDA allows both probabilistic and non-deterministic branching, generalising the classical notion of pushdown automata…
We use the class of commuting quantum computations known as IQP (Instantaneous Quantum Polynomial time) to strengthen the conjecture that quantum computers are hard to simulate classically. We show that, if either of two plausible…
The computational complexity of polynomial ideals and Gr\"obner bases has been studied since the 1980s. In recent years, the related notions of polynomial subalgebras and SAGBI bases have gained more and more attention in computational…
We study the verification of distributed systems where processes are finite automata with access to a shared pool of locks. We consider objectives that are boolean combinations of local regular constraints. We show that the problem,…
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
We propose and investigate a probabilistic model of sublinear-time one-dimensional cellular automata. In particular, we modify the model of ACA (which are cellular automata that accept if and only if all cells simultaneously accept) so that…
Many constructions in computability theory rely on "time tricks". In the higher setting, relativising to some oracles shows the necessity of these. We construct an oracle~$A$ and a set~$X$, higher Turing reducible to~$X$, but for which…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle. This…
Probabilistic timed automata (PTAs) are timed automata (TAs) extended with discrete probability distributions.They serve as a mathematical model for a wide range of applications that involve both stochastic and timed behaviours. In this…
The theory of computer science is based around Universal Turing Machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of UTMs. The nondeterministic polynomial (NP) time…