Related papers: Combining Determinism and Indeterminism
A real number is called left-computable if there exists a computable increasing sequence of rational numbers converging to it. In this article we investigate the Kolmogorov complexity and the binary expansions of a very specific subset of…
Nielsen [quant-ph/0108020] introduced a model of quantum computation by measurement-based simulation of unitary computations. In this model, a consequence of the non-determinism of quantum measurement is the probabilistic termination of…
Computational entropies provide a framework for quantifying uncertainty and randomness under computational constraints. They play a central role in classical cryptography, underpinning the analysis and construction of primitives such as…
We present a natural extension of the process of taking a group quotient to arbitrary subgroups. We first review basic concepts from group theory. This will allow us to see the relationship between our new, more general quotient operation…
We construct examples of finitely generated decidable group presentations that satisfy certain combinations of solvability for the word problem, solvability for the bounded word problem, and computablity for the Dehn function. We prove that…
As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
For any set $A$ of natural numbers with positive upper Banach density and any $k\geq 1$, we show the existence of an infinite set $B\subset{\mathbb N}$ and a shift $t\geq0$ such that $A-t$ contains all sums of $m$ distinct elements from $B$…
If a quantum experiment includes random processes, then the results of repeated measurements can appear consistent with irreversible decoherence even if the system's evolution prior to measurement was reversible and unitary. Two thought…
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
In Diagonally Non-Computable Functions and Bi-Immunity, Carl Jockusch and Andrew Lewis proved that every DNC function computes a bi-immune set. They asked whether every DNC function computes an effectively bi-immune set. We construct a DNC…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…
Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the…
In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…
We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of…
A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely,…