Computational complexity with experiments as oracles

E Beggs, JF Costa, B Loff… - Proceedings of the …, 2008 - royalsocietypublishing.org
… an oracle reveals the need for a theory of oracles whose queries involve errors, time and
other resources, and non-determinism. We analyse the complexity of computationscomplexity

Computational complexity with experiments as oracles. II. Upper bounds

E Beggs, JF Costa, B Loff… - Proceedings of the …, 2009 - royalsocietypublishing.org
… physical experiment as a new form of oracle. We focused on the design and operation of these
computational … with such physical oracles? In Beggs et al. (2008a), we chose a particular …

[PDF][PDF] Physical Experiments as Oracles.

EJ Beggs, JF Costa, JV Tucker - Bull. EATCS, 2009 - academia.edu
… Here we will concentrate on the theory of using a physical experiment as an oracle to an …
of computational complexity. Suppose we wish to study the complexity of computations by …

The impact of models of a physical oracle on computational power

EJ Beggs, JF Costa, JV Tucker - Mathematical Structures in …, 2012 - cambridge.org
… Using physical experiments as oracles for algorithms, we can characterise the … actually
studying T-computability and T-computational complexity. Our approach has been applied in a …

Axiomatizing physical experiments as oracles to algorithms

EJ Beggs, JF Costa, JV Tucker - … Transactions of the …, 2012 - royalsocietypublishing.org
… of computation with physical oracles. We develop three sets of axioms for experimental
characterization theorems of the power of experiments as oracles. The axioms specify the …

The complexity of large-scale convex programming under a linear optimization oracle

G Lan - arXiv preprint arXiv:1309.5550, 2013 - arxiv.org
… We also demonstrate through our preliminary numerical experiments that one of these new
… lower complexity bounds for solving different classes of CP problems under an LO oracle in …

Computations with oracles that measure vanishing quantities

E Beggs, JF Costa, D Poças, JV Tucker - Mathematical Structures in …, 2017 - cambridge.org
… in which physical experiments that measure quantities can be used as oracles to algorithms
… the computational power of various forms of experiment using non-uniform complexity

Classifying the computational power of stochastic physical oracles

E Beggs, P Cortez, JF Costa, JV Tucker - 2018 - repositorio.ulisboa.pt
… with regard to physical accuracy or computational complexity. Even in kinematic systems …
F(σ), so if we make ξ oracle calls, the number of times α that the experiment returns ‘yes’ is a …

[PDF][PDF] Comparing complexity classes relative to physical oracles

E Beggs, JF Costa, JV Tucker - … 6th Conference on Computability in Europe …, 2010 - Citeseer
… We develop the idea of using a physical experiment as an oracle to an algorithm. Of particular
… theories place strong restrictions on computational complexity with physical oracles; …

On the complexity of trial and error

X Bei, N Chen, S Zhang - Proceedings of the forty-fifth annual ACM …, 2013 - dl.acm.org
… extensively in product design and experiments [32]. Generally … two oracles, the verification
oracle and the computation oracle … notation in computational complexity theory for complexity …