Related papers: Conditional Complexity Hardness: Monotone Circuit …
A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
We present an standard constraints generation algorithm to find an explicit set whose robustness is equal to the robustness of the feasible solution set of a combinatorial optimization problem with cost uncertainty. Computational experience…
Optimizing the size and depth of CNOT circuits is an active area of research in quantum computing and is particularly relevant for circuits synthesized from the Clifford + T universal gate set. Although many techniques exist for finding…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…
We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy…
Arithmetic circuits are a natural well-studied model for computing multivariate polynomials over a field. In this paper, we study planar arithmetic circuits. These are circuits whose underlying graph is planar. In particular, we prove an…
Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and QUANTIFIED SAT or, more generally, QUANTIFIED CSP, are FPT…
I will discuss the recent proof that the complexity class NEXP (nondeterministic exponential time) lacks nonuniform ACC circuits of polynomial size. The proof will be described from the perspective of someone trying to discover it.
In recent years it has become popular to study dynamic problems in a sensitivity setting: Instead of allowing for an arbitrary sequence of updates, the sensitivity model only allows to apply batch updates of small size to the original input…
First of all we give some reasons that "natural proofs" built not a barrier to prove P $\not=$ NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the…
In this note, we propose a framework for proving computational lower bounds in norm approximation by leveraging a reverse detection--estimation gap. The starting point is a testing problem together with an estimator whose error is…
Comparator circuits are a natural circuit model for studying bounded fan-out computation whose power sits between nondeterministic branching programs and general circuits. Despite having been studied for nearly three decades, the first…
We present a general framework for good CNF-representations of boolean constraints, to be used for translating decision problems into SAT problems (i.e., deciding satisfiability for conjunctive normal forms). We apply it to the…
Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
We prove a lower bound of $\Omega(n^{1/2 - c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This…
We describe and motivate a proposed new approach to lowerbounding the circuit complexity of boolean functions, based on a new formalization of "patterns" as elements of a special basis of the vector space of all truth table properties. We…
A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars,…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…