Related papers: Randomisation and Derandomisation in Descriptive C…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
We examine a parameterized complexity class for randomized computation where only the error bound and not the full runtime is allowed to depend more than polynomially on the parameter, based on a proposal by Kwisthout in [15,16]. We prove…
We study pseudorandomness and pseudorandom generators from the perspective of logical definability. Building on results from ordinary derandomization and finite model theory, we show that it is possible to deterministically construct, in…
We consider a minimal extension of the language of arithmetic, such that the bounded formulas provably total in a suitably-defined theory \`a la Buss (expressed in this new language) precisely capture polytime random functions. Then, we…
We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…
We introduce a new logic, called \emph{cluster first-order logic}, a restricted fragment of first-order logic specifically designed to study order invariance. An order-invariant formula is one on a vocabulary that contains an order;…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
The search for a logic capturing PTIME is a long standing open problem in finite model theory. One of the most promising candidate logics for this is Choiceless Polynomial Time with counting (CPT). Abstractly speaking, CPT is an…
We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…
One of the cornerstones of the distributed complexity theory is the derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any randomized LOCAL algorithm that solves a locally checkable labeling problem (LCL) can be…
Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and…
We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $\mathsf{BPTIME}$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
We look at classes of languages associated to the fragment of first-order logic B{\Sigma}1 which disallows quantifier alternations. Each class is defined by choosing the set of predicates on positions that may be used. Two key such…
We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class. An enumeration problem belongs to Constant-Delaylin if for an input of size n it…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixed-point logic with counting by a rank operator over prime fields. We show that the…