New Upper Bounds for Trace Reconstruction

We improve the lower bound on worst case trace reconstruction from $\Omega\left(\frac{n^{5/4}}{\sqrt{\log n}}\right)$ to $\Omega\left(\frac{n^{3/2}}{\log^{7} n}\right)$. As a consequence, we improve the lower bound on average case trace reconstruction from $\Omega\left(\frac{\log^{9/4}n}{\sqrt{\log\log n}}\right)$ to $\Omega\left(\frac{\log^{5/2}n}{(\log\log n)^{7}}\right)$.

[1]  John Michael Robson.  Separating Strings with Small Automata , 1989, Inf. Process. Lett..

[2]  Yuval Peres,et al.  Average-Case Reconstruction for the Deletion Channel: Subpolynomially Many Traces Suffice , 2017, 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS).

[3]  Rocco A. Servedio,et al.  Polynomial-time trace reconstruction in the smoothed complexity model , 2020, ArXiv.

[4]  Zachary Chase.  A New Upper Bound for Separating Words , 2020, ArXiv.

[5]  Peter Borwein,et al.  Computational Excursions in Analysis and Number Theory , 2002 .

[6]  Rina Panigrahy,et al.  Trace reconstruction with constant deletion probability and related results , 2008, SODA '08.

[7]  Miroslav Dudík,et al.  Reconstruction from subsequences , 2003, J. Comb. Theory A.

[8]  Tamás Erdélyi,et al.  Littlewood‐Type Problems on [0,1] , 1999 .

[9]  Yuval Peres,et al.  Trace reconstruction with exp(O(n1/3)) samples , 2017, STOC.

[10]  Yuval Peres,et al.  Subpolynomial trace reconstruction for random strings and arbitrary deletion probability , 2018, COLT.

[11]  Olgica Milenkovic,et al.  Coded Trace Reconstruction , 2019, 2019 IEEE Information Theory Workshop (ITW).

[12]  Ryan O'Donnell,et al.  Optimal mean-based algorithms for trace reconstruction , 2017, STOC.

[13]  Russell Lyons,et al.  Lower bounds for trace reconstruction , 2018, ArXiv.

[14]  Rocco A. Servedio,et al.  Efficient average-case population recovery in the presence of insertions and deletions , 2019, APPROX-RANDOM.

[15]  Rocco A. Servedio,et al.  Beyond Trace Reconstruction: Population Recovery from the Deletion Channel , 2019, 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS).

[16]  Tamás Erdélyi,et al.  LITTLEWOOD-TYPE PROBLEMS ON SUBARCS OF THE UNIT CIRCLE , 1997 .

[17]  Shyam Narayanan,et al.  Population Recovery from the Deletion Channel: Nearly Matching Trace Reconstruction Bounds , 2020, ArXiv.

[18]  Zachary Chase.  New lower bounds for trace reconstruction , 2021 .

[19]  Sampath Kannan,et al.  Reconstructing strings from random traces , 2004, SODA '04.

[20]  Cyrus Rashtchian,et al.  Reconstructing Trees from Traces , 2019, COLT.

[21]  Bruce Spang,et al.  Coded trace reconstruction in a constant number of traces , 2020, 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS).

[22]  Shyam Narayanan,et al.  Circular Trace Reconstruction , 2020, ArXiv.

[23]  Akshay Krishnamurthy,et al.  Trace Reconstruction: Generalized and Parameterized , 2019, ESA.

[24]  Sofya Vorotnikova,et al.  Trace Reconstruction Revisited , 2014, ESA.