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Quantum Randomness and Nondeterminism [article]

E. Knill
1996 arXiv   pre-print
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power?  ...  Although reasonable quantum random sources do not add computational power, the discussion of quantum randomness naturally leads to several definitions of the complexity of quantum states.  ...  The computation must be error-free to guarantee this. This type of nondeterminism is at least as powerful as the classical version.  ... 
arXiv:quant-ph/9610012v1 fatcat:mjn6sq7afzgvppatzrcd7zpvce

On nondeterminism in parallel computation

Patrick W. Dymond
1986 Theoretical Computer Science  
Differences in the effects of adding nondeterminism to parallel machines can be traced to the amount of nondeterminism available at each time step.  ...  Nondeterministic parallel complexity classes are investigated using two different nondeterministic versions of the hardware modification machine model.  ...  Much of the power of HMM's lies in their ability to efficiently 'grow' and modify data structures such as linked lists and trees. Examples of this can be found in [6] .  ... 
doi:10.1016/0304-3975(86)90139-8 fatcat:u5pta5hk6jh6jlxijc2zrobtpy

An Approach to Nondeterminism in Translation of CZ Set Theory into Martin-Löf 's Theory of Types

Hassan Haghighi, Seyyed Hassan Mirian Hosseinabadi
2006 Electronical Notes in Theoretical Computer Science  
Due to the high level of abstraction involved in formal specification of software systems, nondeterminism comes as an inevitable part of formal specifications.  ...  Keywords: formal program development, nondeterminism in CZ language, nondeterminism in Martin-Löf's theory of types, translation of CZ set theory into Martin-Löf's theory of types 1  ...  Hence, it seems that we can easily extend ξ to translate nondeterminate constructs; however, to show the power of new mechanism and also the equivalence between our approach and that of [32] , we should  ... 
doi:10.1016/j.entcs.2005.12.065 fatcat:cb2ufjp5yjcaxmjecmxmid43jy

Underspecification, Inherent Nondeterminism and Probability in Sequence Diagrams [chapter]

Atle Refsdal, Ragnhild Kobro Runde, Ketil Stølen
2006 Lecture Notes in Computer Science  
This paper investigates the use of underspecification, inherent nondeterminism and probability in sequence diagrams, the relationships between these concepts, and how these are expressed in STAIRS and  ...  One is to express underspecification, which means that the specifier for the same environment behavior allows several alternative behaviors of the specified component and leaves the choice between these  ...  The research on which this paper reports has been partly carried out within the context of the IKT-2010 project SARDAS (15295/431) and the IKT SOS project ENFORCE (164382/V30), both funded by the Research  ... 
doi:10.1007/11768869_12 fatcat:pfyimn3h2ber5kbfswascbqrzi

Alternating states for dual nondeterminism in imperative programming

Wim H. Hesselink
2010 Theoretical Computer Science  
Results of Morris indicate, however, that the natural domain for the combination of demonic and angelic choice is the free distributive completion (FDC) of the state space.  ...  We therefore determine the duality function from the FDC to the dual of the FDC of the dual ordered set. The elements of the FDC are classified according to their conjunctivity and disjunctivity.  ...  The combination of demonic and angelic nondeterminism was first proposed in 1981, for the alternating Turing machines of [9] . Here both forms of nondeterminism were bounded.  ... 
doi:10.1016/j.tcs.2010.03.016 fatcat:mdtkgn7xsjas7lmorrguzcjtpu

On-the-Fly Confluence Detection for Statistical Model Checking [chapter]

Arnd Hartmanns, Mark Timmer
2013 Lecture Notes in Computer Science  
We evaluate our approach, which is implemented as part of the modes simulator for the MODEST modelling language, on a set of examples that highlight its strengths and limitations and show the improvements  ...  In contrast to previous approaches that use partial order reduction, the confluence-based technique can handle additional kinds of nondeterminism.  ...  Related work Aside from [3] and an approach that focuses on planning problems and infinite-state models [12] , the only other solution to the problem of nondeterminism in SMC that we are aware of is  ... 
doi:10.1007/978-3-642-38088-4_23 fatcat:k43ugk56unaxxizewo5ltgrxa4

Passes, sweeps and visits [chapter]

Joost Engelfriet, Gilberto Filè
1981 Lecture Notes in Computer Science  
In section 3 a comparison of the formal power of the classes is made: (i) corresponding pure and simple classes have the same power, (ii) the formal power increases in this order: passes, alternating  ...  D Our second result compares the power of visits, sweeps, alter.passes, and passes, and considers the influence on power of increasing k.  ... 
doi:10.1007/3-540-10843-2_16 fatcat:2qk7qf6nu5hs3hg6xylzonllka

Algebraic approaches to nondeterminism---an overview

Michał Walicki, Sigurd Meldal
1997 ACM Computing Surveys  
However, there is no standard definition of this notion. In this section we sketch the main alternatives of modeling operations and homomorphisms using power-set structures.  ...  The alternative ͑1Ј͒ f͑ x 1 , x 2 , x 3 ͒ ՞ .͕ x 1 , x 2 , x 3 ͖ ͑2Ј͒ f͑0, 1, 2͒ ϭ .͕0, 1͖ will ensure that the result set of f(0, 1, 2) is the join of 0 and 1 and does not include 2.  ... 
doi:10.1145/248621.248623 fatcat:5o2gkoijefg7dgznddcqefpkbi

Good for Games Automata: From Nondeterminism to Alternation

Udi Boker, Karoliina Lehtinen, Michael Wagner
2019 International Conference on Concurrency Theory  
The equivalence of these properties has not been formally shown. We generalize all of these definitions to alternating automata and show their equivalence.  ...  We leave open the question of whether alternating GFG automata of stronger acceptance conditions allow for doubly-exponential succinctness compared to deterministic automata.  ...  The next definition comes from the work in [19, 3] on the power of nondeterminism in tree automata.  ... 
doi:10.4230/lipics.concur.2019.19 dblp:conf/concur/BokerL19 fatcat:w6nqhu5o2zcg3j3jcexgyi4s5y

Some Bridging Results and Challenges in Classical, Quantum and Computational Randomness [chapter]

Giuseppe Longo, Catuscia Palamidessi, Thierry Paul
2011 Randomness Through Computation  
The spectacular power of quantum algorithms, on the other side, overcomes this double constraint (randomness of the result and necessity of a posteriori validation of the "guess") and fully justifies this  ...  power of a concurrent language usually lies on the capability to exert such control.  ... 
doi:10.1142/9789814327756_0005 fatcat:axcog2svzneffffynrglc4llpu

Probabilistic may/must testing: retaining probabilities by restricted schedulers

Sonja Georgievska, Suzana Andova
2012 Formal Aspects of Computing  
We also give an alternative characterization of the testing preorder as a probabilistic ready-trace preorder.  ...  point of view of compositionality, in the context of randomized protocols and in probabilistic model checking.  ...  the derivation power of the axioms.  ... 
doi:10.1007/s00165-012-0236-5 fatcat:o5cgwomz35go7b6vzvimu5us3a

Automata with modulo counters and nondeterministic counter bounds

Daniel Reidenbach, Markus L. Schmid
2014 Kybernetika (Praha)  
are nondeterministically guessed, and this is the only element of nondeterminism.  ...  We introduce and investigate Nondeterministically Bounded Modulo Counter Automata (NBMCA), which are two-way one-head automata that comprise a constant number of modulo counters, where the counter bounds  ...  This meets our expectation of nondeterminism being a useful resource enhancing the expressive power of automata.  ... 
doi:10.14736/kyb-2014-1-0066 fatcat:jlu5akepqvdijdnag5qytam4ri

Quantum weakly nondeterministic communication complexity

François Le Gall
2013 Theoretical Computer Science  
In this paper, we prove that, in the framework of communication complexity, even the weak version of quantum nondeterminism is strictly stronger than classical nondeterminism.  ...  Another stronger definition of quantum nondeterminism has already been extensively studied, corresponding to the view of quantum nondeterminism as unbounded-error one-sided quantum computation, but, although  ...  These two views of nondeterminism have been extended to obtain two alternative definitions of quantum nondeterminism.  ... 
doi:10.1016/j.tcs.2012.12.015 fatcat:fs6sk76p5zf2fapaenpq4jfzca

Denotational Models for Unbounded Nondeterminism1 1Work partially supported by the Office of Naval Research

Michael W. Mislove
1995 Electronical Notes in Theoretical Computer Science  
Unbounded nondeterminism has played a fundamental role in the areas of re nement between models of languages supporting real-time constructs and in the treatment o f fairness.  ...  In this paper we explore this issue, and we show that only one of the three powerdomains has a suitable analogue for modeling unbounded nondeterminism.  ...  Q that is continuous. 2 The domain-theoretic approach to modeling nondeterminism is via the use of power domains, w h i c h are analogues of the power set of a set.  ... 
doi:10.1016/s1571-0661(04)00023-4 fatcat:ulafwxxrpvevrgfkxmdywfxrbe

Page 2878 of Mathematical Reviews Vol. , Issue 84g [page]

1984 Mathematical Reviews  
Plotkin gave a denotational semantics for bounded nondeterminism (i.e., a terminating program produces finitely many outputs), using as domains power sets of flat cpo’s [SIAM J.  ...  Combinatorial group properties of principal types of distributed computing system architecture are determined by means of which all possible alternative structures can be enumerated with the aid of the  ... 
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