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Dynamic Complexity of Parity Exists Queries [article]

Nils Vortmeier, Thomas Zeume
2021 arXiv   pre-print
Already this simple query of quantifier structure parity-exists is a major roadblock for dynamically capturing extensions of first-order logic.  ...  Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman  ...  Vol. 17:4 DYNAMIC COMPLEXITY OF PARITY EXISTS QUERIES 9:13 • Before the change, w ∈ N •• (A, B) holds, but not afterwards.  ... 
arXiv:1910.06004v5 fatcat:ymmkwc5xkrdvpkq2afcdf4gada

Dynamic Complexity of Parity Exists Queries

Nils Vortmeier, Thomas Zeume, Michael Wagner
2020 Annual Conference for Computer Science Logic  
Already this simple query of quantifier structure parity-exists is a major roadblock for dynamically capturing extensions of first-order logic.  ...  ACM Subject Classification Theory of computation → Logic and databases; Theory of computation → Complexity theory and logic This simple program proves that Parity is in the dynamic complexity class DynFO  ...  Complexity of Parity Exists Queries Deletions of edges.  ... 
doi:10.4230/lipics.csl.2020.37 dblp:conf/csl/VortmeierZ20 fatcat:huh4qlycbzabtf6y5vur7ijz4i

Testing Dynamic Environments: Back to Basics [article]

Yonatan Nakar, Dana Ron
2021 arXiv   pre-print
We continue the line of work initiated by Goldreich and Ron (Journal of the ACM, 2017) on testing dynamic environments and propose to pursue a systematic study of the complexity of testing basic dynamic  ...  The meta-algorithm has query complexity poly(1/ϵ), is non-adaptive and has one-sided error. We show that all the threshold rules satisfy the set of conditions, and therefore are poly(1/ϵ)-testable.  ...  The aim is to design time-conforming algorithms with low query complexity. Goldreich and Ron [6] investigate the complexity landscape of testing dynamic environments from multiple angles.  ... 
arXiv:2105.00759v2 fatcat:o5v3fuvqvbavnkzsamtx6c2vhq

Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters

Dominic W. Berry, Andrew M. Childs, Robin Kothari
2015 2015 IEEE 56th Annual Symposium on Foundations of Computer Science  
By implementing a linear combination of quantum walk steps with coefficients given by Bessel functions, our algorithm's complexity (as measured by the number of queries and 2-qubit gates) is logarithmic  ...  We present an algorithm for sparse Hamiltonian simulation whose complexity is optimal (up to log factors) as a function of all parameters of interest.  ...  materials Quantum dynamics The dynamics of a quantum system are determined by its Hamiltonian.  ... 
doi:10.1109/focs.2015.54 dblp:conf/focs/BerryCK15 fatcat:q5q5kf7i5jfmjj7rgvkokxlio4

Lower Bounds for Fully Dynamic Connectivity Problems in Graphs

M. R. Henzinger, M. L. Fredman
1998 Algorithmica  
We prove lower bounds on the complexity of maintaining fully dynamic k-edge or k-vertex connectivity in plane graphs and in (k − 1)-vertex connected graphs.  ...  We show an amortized lower bound of (log n/k(log log n + log b)) per edge insertion, deletion, or query operation in the cell probe model, where b is the word size of the machine and n is the number of  ...  We thank an anonymous referee for pointing out the helpful parity prefix sum problem and the above extensions.  ... 
doi:10.1007/pl00009228 fatcat:fuoyf6xrafflnmzyncqunizhxy

Tractable Learning for Complex Probability Queries

Jessa Bekker, Jesse Davis, Arthur Choi, Adnan Darwiche, Guy Van den Broeck
2015 Neural Information Processing Systems  
This allows us to support a broader class of complex probability queries, including counting, threshold, and parity, in polytime.  ...  We propose a tractable learner that guarantees efficient inference for a broader class of queries.  ...  Pr(φ|ψ), where φ, ψ are complex properties, such as counts, thresholds, comparison, and parity of sets of random variables.  ... 
dblp:conf/nips/BekkerDCDB15 fatcat:rxlcxzngmbf5ngcszxdml6ede4

New Lower Bound Techniques for Dynamic Partial Sums and Related Problems

Thore Husfeldt, Theis Rauhe
2003 SIAM journal on computing (Print)  
We study the complexity of the dynamic partial sum problem in the cell-probe model. We give the model access to nondeterministic queries and prove that the problem remains hard.  ...  From these results, we derive a number of lower bounds for dynamic algorithms and data structures: We prove lower bounds for dynamic algorithms for existential range queries, reachability in directed graphs  ...  The authors thank Arne Anderson, Gerth Stølting Brodal, Faith Fich, Peter Bro Miltersen, and Sven Skyum for valuable comments about various aspects of this work.  ... 
doi:10.1137/s0097539701391592 fatcat:ecq6zkwuqbemvhhd42pb5qw3fq

Neural Synchronization based Secret Key Exchange over Public Channels: A survey [article]

Sandip Chakraborty, Jiban Dalal, Bikramjit Sarkar, Debaprasad Mukherjee
2015 arXiv   pre-print
Our survey also discusses queries, heuristics, erroneous information, group key exchange, synaptic depths, etc, that have been proposed to increase the time complexity of algorithmic interception or decoding  ...  The Tree Parity Machine and its variants, neural networks with tree topologies incorporating parity checking of state bits, appear to be one of the most secure and stable models of the end-point networks  ...  These networks constitute a form of dynamic systems which show a variety of complex behaviour including the phenomenon of chaos and synchronization [5] .  ... 
arXiv:1502.05153v1 fatcat:mhxwrtb5xng5fouiyky7rhtmdu

Hardness results for dynamic problems by extensions of Fredman and Saks' chronogram method [chapter]

Thore Husfeldt, Theis Rauhe
1998 Lecture Notes in Computer Science  
We characterise the complexity of maintaining the value of any symmetric function on the prefixes of a bit string. Example: Range queries. We can illustrate our approach using range query problems.  ...  The updates are as before, and the query is parity(i, s): return x1 + · · · + xi mod 2 provided that |s −  ...  Acknowledgements The authors thank Arne Anderson, Gerth Stølting Brodal, Faith Fich, Peter Bro Miltersen, and Sven Skyum for valuable comments about various aspects of this work.  ... 
doi:10.1007/bfb0055041 fatcat:j3qyunz5mneobfiebb7opvvvli

Hardness Results for Dynamic Problems by Extensions of Fredman and Saks' Chronogram Method

Thore Husfeldt, Theis Rauhe
1997 BRICS Report Series  
majority of the prefixes of a string of bits and range queries.  ...  We characterise the complexity of maintaining the value of any symmetric function on the prefixes of a bit string.  ...  Acknowledgements The authors had valuable discussions with Arne Anderson, Gerth Stølting Brodal, Peter Bro Miltersen, and Sven Skyum about various aspects of this work.  ... 
doi:10.7146/brics.v4i32.18958 fatcat:jkmn56byvbezdgwsgw6u2a5kt4

EXPONENTIAL IMPROVEMENT IN PRECISION FOR SIMULATING SPARSE HAMILTONIANS

DOMINIC W. BERRY, ANDREW M. CHILDS, RICHARD CLEVE, ROBIN KOTHARI, ROLANDO D. SOMMA
2017 Forum of Mathematics, Sigma  
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods.  ...  Unlike previous approaches based on product formulas, the query complexity is independent of the number of qubits acted on, and for time-varying Hamiltonians, the gate complexity is logarithmic in the  ...  This work was supported in part by ARC grants FT100100761 and DP160102426, Canada's NSERC, CIFAR, the Ontario Ministry of Research and Innovation, and the US ARO.  ... 
doi:10.1017/fms.2017.2 fatcat:qlsu3upesrazjnxha4se7cxt5q

Analysis of FPGA-Based Reconfiguration Methods for Mobile and Embedded Applications

Darshika G. Perera
2015 Proceedings of the 12th FPGAworld Conference 2015 on - FPGAworld '15  
There are different methods of reconfiguring the hardware on chip dynamically.  ...  In this paper, a 2-D error correction code architecture based on EG-LDPC and single parity check (SPC) code is proposed as a solution to MBU problem of SRAM memories.  ...  There are different methods of reconfiguring the hardware on chip dynamically.  ... 
doi:10.1145/2889287.2889297 fatcat:3xrcz3p7bja2xet4pnxe5re4ki

Hamiltonian simulation with nearly optimal dependence on spectral norm [article]

Guang Hao Low
2018 arXiv   pre-print
The complexity of our algorithm is O((t√(d)H_1 → 2)^1+o(1)/ϵ^o(1)) queries and a factor O(b) more gates, which is shown to be optimal up to subpolynomial factors through a matching query lower bound.  ...  , which matches the quantum search lower bound of Ω(√(d)) queries and improves upon prior art [Berry and Childs, QIP 2010] of Õ(d^2/3) queries.  ...  The stated lower bound is then obtained by combining the known quantum query complexity of Ω(n √ m) [Rei09] for computing PARITY • OR on n × m bits , with parameters that describe H PARITY • OR .  ... 
arXiv:1807.03967v1 fatcat:w6uw4geox5fw5lqfsycuyl3zlq

Lower bounds for dynamic transitive closure, planar point location, and parentheses matching [chapter]

Thore Husfeldt, Theis Rauhe, Søren Skyum
1996 Lecture Notes in Computer Science  
We also show that if the update time is bounded by the product of the worst-case update time and the answer to the query, then the update time must be Ω √ (log n/ log log n) .  ...  We give a lower bound of Ω √ (log n/ log log n) for the dynamic membership problem of any Dyck language with two or more letters.  ...  We use a result of Fredman and Saks [10] that gives a lower bound on the complexity of the prefix parity problem: given a vector x 1 , . . . , x n of bits, maintain a data structure that is able to react  ... 
doi:10.1007/3-540-61422-2_132 fatcat:37f3c4yiznegbiewwhz32jgaay

Lower Bounds for Dynamic Transitive Closure, Planar Point Location, and Parentheses Matching

Thore Husfeldt, Theis Rauhe, Søren Skyum
1996 BRICS Report Series  
We also show that if the update time is bounded by the product of the worst-case update time and the<br />answer to the query, then the update time must be Omega(sqrt(log n/ log log n)).  ...  We give a lower bound of Omega(sqrt(log n/log log n)) for the dynamic membership problem of any Dyck language with two or more letters.  ...  We use a result of Fredman and Saks [10] that gives a lower bound on the complexity of the prefix parity problem: given a vector x 1 , . . . , x n of bits, maintain a data structure that is able to react  ... 
doi:10.7146/brics.v3i9.19972 fatcat:5kq5dctv4jh6fhbbpk3fhcbrgm
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