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- research-articleAugust 2024
- research-articleDecember 2023
Beyond the Existential Theory of the Reals
Theory of Computing Systems (TOCSYS), Volume 68, Issue 2Pages 195–226https://doi.org/10.1007/s00224-023-10151-xAbstractWe show that completeness at higher levels of the theory of the reals is a robust notion (under changing the signature and bounding the domain of the quantifiers). This mends recognized gaps in the hierarchy, and leads to stronger completeness ...
- research-articleJuly 2023
A Characterization of Functions over the Integers Computable in Polynomial Time Using Discrete Ordinary Differential Equations
AbstractThis paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and algorithm ...
- research-articleJuly 2023
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- research-articleApril 2023
- research-articleJanuary 2023
On the absolute and relative oriented clique problems’ time complexity
Procedia Computer Science (PROCS), Volume 223, Issue CPages 275–282https://doi.org/10.1016/j.procs.2023.08.238AbstractLet ⃗G = (V, A) be an oriented graph. An oriented k-coloring of ⃗G is a partition of V into k color classes, such that there is no pair of adjacent vertices belonging to the same class and all the arcs between a pair of color classes have the same ...
- research-articleDecember 2022
- research-articleDecember 2022
Quadratic Lower Bounds for Algebraic Branching Programs and Formulas
AbstractWe show that any Algebraic Branching Program (ABP) computing the polynomial has at least vertices. This improves upon the lower bound of , which follows from the classical result of Strassen (1973a) and Baur & Strassen (1983)...
- research-articleNovember 2022
- research-articleAugust 2022
Ergodic Theorems and Converses for PSPACE Functions
Theory of Computing Systems (TOCSYS), Volume 67, Issue 3Pages 491–520https://doi.org/10.1007/s00224-022-10094-9AbstractWe initiate the study of effective pointwise ergodic theorems in resource-bounded settings. Classically, the convergence of the ergodic averages for integrable functions can be arbitrarily slow (Krengel Monatshefte Für Mathematik 86, 3–6 1978). In ...
- research-articleAugust 2022
Bad and Good News for Strassen’s Laser Method: Border Rank of and Strict Submultiplicativity
- research-articleJune 2022
Amplification with One NP Oracle Query
AbstractWe provide a complete picture of the extent to which amplification of success probability is possible for randomized algorithms having access to one NP oracle query, in the settings of two-sided, onesided, and zero-sided error. We generalize this ...
- research-articleMay 2022
Completeness for the Complexity Class and Area-Universality
- research-articleApril 2022
Interference Aware Workload Scheduling for Latency Sensitive Tasks in Cloud Environment
AbstractThe virtualization technology enhances resource utilization and scalability in the cloud environment. Multiple virtual machines with divergent specifications in terms of hardware and software can be run on a single physical machine. Performance of ...
- research-articleJanuary 2022
When Symmetries Are Not Enough: A Hierarchy of Hard Constraint Satisfaction Problems
SIAM Journal on Computing (SICOMP), Volume 51, Issue 2Pages 175–213https://doi.org/10.1137/20M1383471We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction---a refinement of the Hrushovski-encoding---to $\omega$-categorical structures in a possibly infinite signature. We show that the encoded ...
- research-articleJanuary 2022
The Complexity of Necklace Splitting, Consensus-Halving, and Discrete Ham Sandwich
SIAM Journal on Computing (SICOMP), Volume 52, Issue 2Pages STOC19-200–STOC19-268https://doi.org/10.1137/20M1312678We resolve the computational complexity of three problems known as Necklace Splitting, Consensus-Halving, and Discrete Ham sandwich, showing that they are PPA-complete. For NECKLACE SPLITTING, this result is specific to the important special case in which ...
- research-articleJanuary 2022
A Short List of Equalities Induces Large Sign-Rank
SIAM Journal on Computing (SICOMP), Volume 51, Issue 3Pages 820–848https://doi.org/10.1137/19M1271348We exhibit a natural function $F_n$ on $n$ variables that can be computed by just a linear-size decision list of “Equalities,” but whose sign-rank is $2^{\Omega(n^{1/4})}$. This yields the following two new unconditional complexity class separations. 1. ...
- research-articleDecember 2021