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We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…

The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see…

We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…

Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…

The presence of symmetries is one of the central structural features that make some integer programs challenging for state-of-the-art solvers. In this work, we study the efficacy of Linear Programming (LP) hierarchies in the presence of…

Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…

We prove that if the linear-time and polynomial-time hierarchies coincide, then every model of $\Pi_1(\mathbb{N}) + \neg \Omega_1$ has a proper end-extension to a model of $\Pi_1(\mathbb{N})$, and so $\Pi_1(\mathbb{N}) + \neg \Omega_1…

In 2008, Bodirsky and Grohe showed that for every $\Pi_n^{\mathrm{P}}$-level of the Polynomial Hierarchy (PH) there are $\omega$-categorical Constraint Satisfaction Problems (CSPs) complete for this level. We show that, in fact, there are…

We show that the techniques for resource control that have been developed in the so-called "light logics" can be fruitfully applied also to process algebras. In particular, we present a restriction of Higher-Order pi-calculus inspired by…

We introduce a generalization of Selman's P-selectivity that yields a more flexible notion of selectivity, called (polynomial-time) multi-selectivity, in which the selector is allowed to operate on multiple input strings. Since our…

Valiant introduced matchgate computation and holographic algorithms. A number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time. We show that, in a very strong sense, matchgate…

This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative…

In this work we study oblivious complexity classes. These classes capture the power of interactive proofs where the prover(s) are only given the input size rather than the actual input. In particular, we study the connections between the…

A polyomino is a polygonal region with axis parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling and packing problems with polyomino pieces and a polyomino container $P$. We give…

A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.

Courcelle's famous theorem from 1990 states that any property of graphs definable in monadic second-order logic (MSO) can be decided in linear time on any class of graphs of bounded treewidth, or in other words, MSO is fixed-parameter…

Finding the length of the longest increasing subsequence (LIS) is a classic algorithmic problem. Let $n$ denote the size of the array. Simple $O(n\log n)$ algorithms are known for this problem. We develop a polylogarithmic time randomized…

The satisfiability problem of the branching time logic CTL is studied in terms of computational complexity. Tight upper and lower bounds are provided for each temporal operator fragment. In parallel, the minimal model size is studied with a…

Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial…

We introduce the idea that the P vs NP problem can have a finer structure. Given the NP complete problem of interest, the configurations space of the problem can be divided in (at least) two regions. In one region, polynomial algorithms to…