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Nondeterministic State Complexity of Positional Addition

Galina Jirásková, Alexander Okhotin
2009 Electronic Proceedings in Theoretical Computer Science  
Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits.  ...  It is proved that if two sets of numbers S and T are represented by nondeterministic automata of m and n states, respectively, then their sum s+t | s in S, t in T is represented by a nondeterministic automaton  ...  For every k 9, the nondeterministic state complexity of positional addition is given by the function f k (m, n) = 6, if m = n = 1, 2mn + 2m + 2n + 1, if m + n 3.  ... 
doi:10.4204/eptcs.3.14 fatcat:mxhc7t7fjrhzzfur254kmja3hy

Quantum weakly nondeterministic communication complexity

François Le Gall
2013 Theoretical Computer Science  
More precisely, we show the first separation, for a total function, of quantum weakly nondeterministic and classical nondeterministic communication complexity.  ...  In this paper, we study a weak version of quantum nondeterministic communication complexity, corresponding to the most natural generalization of classical nondeterminism, in which a classical proof has  ...  Bob rotates it by the angle of −yπ/2 n , obtaining the state 1 √ 2 (cos (x − y)π 2 n |0 + sin (x − y)π 2 n |1 ). Measuring this state gives 1 with positive probability if x = y.  ... 
doi:10.1016/j.tcs.2012.12.015 fatcat:fs6sk76p5zf2fapaenpq4jfzca

Quantum Weakly Nondeterministic Communication Complexity [article]

Francois Le Gall
2006 arXiv   pre-print
We show the first separation between classical nondeterministic communication complexity and this model of quantum nondeterministic communication complexity for a total function.  ...  We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol.  ...  Bob rotates it by the angle of −yπ/2 n , obtaining the state 1 √ 2 (cos (x − y)π 2 n |0 + sin (x − y)π 2 n |1 ). Measuring this state gives 1 with positive probability if x = y.  ... 
arXiv:quant-ph/0511025v3 fatcat:t2elbkodxfaofluwe3udgcgibi

Quantum Weakly Nondeterministic Communication Complexity [chapter]

François Le Gall
2006 Lecture Notes in Computer Science  
More precisely, we show the first separation, for a total function, of quantum weakly nondeterministic and classical nondeterministic communication complexity.  ...  In this paper, we study a weak version of quantum nondeterministic communication complexity, corresponding to the most natural generalization of classical nondeterminism, in which a classical proof has  ...  Bob rotates it by the angle of −yπ/2 n , obtaining the state 1 √ 2 (cos (x − y)π 2 n |0 + sin (x − y)π 2 n |1 ). Measuring this state gives 1 with positive probability if x = y.  ... 
doi:10.1007/11821069_57 fatcat:hrvegkg5cnb4ha5fujo5jxkyz4

One-Way Communication Complexity and the Nečiporuk Lower Bound on Formula Size

Hartmut Klauck
2007 SIAM journal on computing (Print)  
amount of nondeterministic guesses, and formulae allowed a logarithmic factor of non-Communication Complexity and the Nečiporuk Method 3 deterministic guesses more.  ...  for limited nondeterministic and for quantum communication complexity.  ...  The nondeterministic communication complexity N (f ) is the complexity of an optimal one-way protocol for f using arbitrarily many nondeterministic bits.  ... 
doi:10.1137/s009753970140004x fatcat:nnlcg6twr5e4tgtftlfip6eiqu

Properties and Application of Nondeterministic Quantum Query Algorithms [article]

Alina Dubrovska Vasilieva
2006 arXiv   pre-print
We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity.  ...  We introduce a fresh notion in addition to already studied nondeterministic algorithms and introduce dual nondeterministic quantum query algorithms.  ...  complexities of nondeterministic and exact algorithms for several classes of Boolean functions.  ... 
arXiv:quant-ph/0606248v1 fatcat:po3ytkopfffdbofg5wpi2tkqiq

One-way communication complexity and the Neciporuk lower bound on formula size [article]

Hartmut Klauck
2004 arXiv   pre-print
We investigate the scenarios of probabilistic formulae, nondeterministic formulae, and quantum formulae.  ...  Regarding communication complexity we give optimal separations between one-way and two-way protocols in the cases of limited nondeterministic and quantum communication, and we show that zero-error quantum  ...  The nondeterministic communication complexity N (f ) is the complexity of an optimal one-way protocol for f using arbitrarily many nondeterministic bits.  ... 
arXiv:cs/0111062v2 fatcat:ycnaen7igje2pkw75v6syfjukq

Space bounded computations: review and new separation results

Desh Ranjan, Richard Chang, Juris Hartmanis
1991 Theoretical Computer Science  
We show that, for a slightly modified Turing machine model, low level deterministic and nondeterministic space bounded complexity classes are different.  ...  We conclude by enLmerating open problems which arise out of the discussion.  ...  The first author would like to thank the students of the Spring 1989 class of CS782 31)2 D Ranlan et al. at Cornell University/for listening to some of the ideas presented in this paper and providing constructive  ... 
doi:10.1016/0304-3975(91)90391-e fatcat:xxm3hj5hwncsre7kavd4wbptbq

Computational limitations of Stochastic Turing machines and Arthur-Merlin games with small space bounds [chapter]

Maciej Liśkiewicz, Rüdiger Reischuk
1997 Lecture Notes in Computer Science  
We give an overview on complexity classes dened by STMs with space resources between constant and logarithmic size and constant or sublinear bounds on the number of alternations.  ...  A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types.  ...  Since it is also shown that the time complexity of an stochastic automata recognizing CENTER cannot be polynomial it seems unlikely that the number of rounds required for this language can be improved  ... 
doi:10.1007/bfb0029952 fatcat:7vnbstfpxngkpooer65mvnr7ne

L versus P

Frank Vega
2020 Zenodo  
This conjecture states that every even integer greater than 2 can be written as the sum of two primes.  ...  In addition, we demonstrate that L is equal to NSPACE(S(n)) for some S(n) = o(log n). In this way, we show the complexity class L is not equal to P.  ...  In addition, we can reduce in a nondeterministic constant space the language L G to L SG just nondeterministically inserting the blank symbol # within two arbitrary positions between the 0's on the input  ... 
doi:10.5281/zenodo.3659820 fatcat:kl7kofe6gvhedkaayzb6n4bz3q

Space bounded computations : Review and new separation results [chapter]

J. Hartmanis, Desh Ranjan
1989 Lecture Notes in Computer Science  
We show that, for a slightly modified Turing machine model, low level deterministic and nondeterministic space bounded complexity classes are different.  ...  We also present other changes in the computation model which bring out and clarify the importance of space constructibility. We conclude by enumerating open problems which arise out of the discussion.  ...  Next, we show that deterministic machines do not gain any additional computational power from the dot capability. We state just a special case of this result.  ... 
doi:10.1007/3-540-51486-4_56 fatcat:ygieduf6zzahbaflfffs4afpfu

L versus P

Frank Vega
2020 Zenodo  
This conjecture states that every even integer greater than 2 can be written as the sum of two primes.  ...  In addition, we demonstrate that L is equal to NSPACE(S(n)) for some S(n) = o(log n). In this way, we show the complexity class L is not equal to P.  ...  In addition, we can reduce in a nondeterministic constant space the language L G to L SG just nondeterministically inserting the blank symbol # within two arbitrary positions between the 0's on the input  ... 
doi:10.5281/zenodo.3660149 fatcat:55awxu6dknbpvoghybtxxi637q

A speed-up theorem without tape compression

Viliam Geffert
1993 Theoretical Computer Science  
We shall show that, for each nondeterministic single-tape Turing machine M of time complexity T(n)> n2 and each K 2 1, there exists an equivalent K times faster nondeterministic Turing machine M' writing  ...  Therefore, nondeterministic single-tape Turing machines do not require tape compression for speeding up.  ...  its tape of time complexity T'(n)<e.  ... 
doi:10.1016/0304-3975(93)90362-w fatcat:acrdfwzie5hlzevhd6xcusvnlq

Nondeterministic Strategies and their Refinement in Strategy Logic

Giuseppe De Giacomo, Bastien Maubert, Aniello Murano
2020 Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning  
For instance, given a nondeterministic strategy that allows only safe executions, refine it to, additionally, eventually reach a desired state of affairs.  ...  We show that model checking this logic can be done at no additional computational cost with respect to standard SL, and can be used to solve a variety of problems such as synthesis of maximally permissive  ...  For instance, given a nondeterministic strategy that allows only safe executions, one may want to refine it to, in addition, be sure to eventually reach a desired state of affairs.  ... 
doi:10.24963/kr.2020/30 dblp:conf/kr/GiacomoMM20 fatcat:pgdpcdn22vgybhlgiktuq7xy6i

The Complexity of Number Theory

Frank Vega
2020 Zenodo  
This conjecture states that every even integer greater than 2 can be written as the sum of two primes. This is known as the strong Goldbach's conjecture.  ...  The conjecture that all odd numbers greater than 7 are the sum of three odd primes is known today as the weak Goldbach conjecture. A principal complexity class is NSPACE(S(n)) for some S(n).  ...  In addition, we can reduce in a nondeterministic constant space the language L W G to L W SG just nondeterministically inserting the blank symbol # within two arbitrary positions between the 0's on the  ... 
doi:10.5281/zenodo.3692809 fatcat:q5f4ojnyv5eerlr5hej5ki7uie
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