Related papers: Ray tracing -- computing the incomputable?
We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions…
Computational and complexity theory are core components of the computer science curriculum, and in the vast majority of cases are taught using decision problems as the main paradigm. For experienced practitioners, decision problems are the…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
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…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and…
We identify "proper quantum computation" with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish "no-go" theorems for classes of quantum optical experiments…
This thesis is intended in part to summarize and also to contribute to the newest developments in passive linear optics that have resulted, directly or indirectly, from the somewhat shocking discovery in 2010 that the BosonSampling problem…
The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here…
By means of a simple example it is demonstrated that the task of finding and identifying certain patterns in an otherwise (macroscopically) unstructured picture (data set) can be accomplished efficiently by a quantum computer. Employing the…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We harness the power of Bayesian emulation techniques, designed to aid the analysis of complex computer models, to examine the structure of complex Bayesian analyses themselves. These techniques facilitate robust Bayesian analyses and/or…
Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints - like…
We prove that if our calculating capability is that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.
With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to…
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to…
Self-replication is central to all life, and yet how it dynamically emerges in physical, non-equilibrium systems remains poorly understood. Von Neumann's pioneering work in the 1940s and subsequent developments suggest a natural hypothesis:…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
We study the paradoxical aspects of closed time-like curves and their impact on the theory of computation. After introducing the $\text{TM}_\text{CTC}$, a classical Turing machine benefiting CTCs for backward time travel, Aaronson et al.…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…