Related papers: Oblivious Complexity Classes Revisited: Lower Boun…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory V$^0_2$ is consistent with the conjecture that NEXP…
We show that a large fraction of the data-structure lower bounds known today in fact follow by reduction from the communication complexity of lopsided (asymmetric) set disjointness. This includes lower bounds for: * high-dimensional…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…
Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. S{\'e}nizergues and the fifth author (ICALP2018) proved that the isomorphism problem for virtually free groups is…
The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by…
This paper proves the NP-completeness of the reachability problem for the class of flat counter machines with difference bounds and, more generally, octagonal relations, labeling the transitions on the loops. The proof is based on the fact…
We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…
We investigate the problem of identifying database repairs for missing tuples in query answers. We show that when the query is part of the input - the combined complexity setting - determining whether or not a repair exists is…
We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of…
Cai and Hemachandra used iterative constant-setting to prove that Few $\subseteq$ $\oplus$P (and thus that FewP $\subseteq$ $\oplus$P). In this paper, we note that there is a tension between the nondeterministic ambiguity of the class one…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
A fundamental question in computer science is: Is it harder to solve $n$ instances independently than to solve them simultaneously? This question, known as the direct sum question or direct sum theorem, has been paid much attention in…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
The distinguishing result of this paper is a $\mathbf{P}$-time enumerable partition of all the potential perfect matchings in a bipartite graph. This partition is a set of equivalence classes induced by the missing edges in the potential…