Regular games provide a very useful model for the synthesis of controllers in reactive systems. The complexity of these games depends on the representation of the winning condition: if it is represented through a win-set, a coloured condition, a Zielonka-DAG or Emerson-Lei formulae, the winner problem is PSPACE-complete; if the winning condition is represented as a Zielonka tree, the winner pro...

In 1996, Fredman and Khachiyan [J. Algorithms 21 (1996) 618–628] presented a remarkable algorithm for the problem of checking the duality of a pair of monotone Boolean expressions in disjunctive normal form. Their algorithm runs in no(logn) time, thus giving evidence that the problem lies in an intermediate class between P and co-NP. In this paper we show that a modified version of their algori...

A fast consistency prover is a consistent poly-time axiomatized theory that has short proofs of the finite consistency statements of any other poly-time axiomatized theory. Kraj́ıček and Pudlák proved in [5] that the existence of an optimal propositional proof system is equivalent to the existence of a fast consistency prover. It is an easy observation that NP = coNP implies the existence of a f...

We study the problem of consistent query answering under primary key violations. In this setting, the relations in a database violate the key constraints and we are interested in maximal subsets of the database that satisfy the constraints, which we call repairs. For a boolean query Q, the problem CERTAINTY(Q) asks whether every such repair satisfies the query or not; the problem is known to be...

This paper reports on our ongoing work that aims at a classification of conjunctive queries q according to the data complexity of answering ontologymediated queries ({A v T t F}, q). We give examples of queries from the complexity classes C ∈ {AC, L, NL, P, CONP}, and obtain a few syntactical conditions for C-membership and C-hardness.

Via competing provers, we show that if a language A is self-reducible and has polynomial-size circuits then S2 = S2. Building on this, we strengthen the Kämper– AFK Theorem, namely, we prove that if NP ⊆ (NP ∩ coNP)/poly then the polynomial hierarchy collapses to SNP∩coNP 2 . We also strengthen Yap’s Theorem, namely, we prove that if NP ⊆ coNP/poly then the polynomial hierarchy collapses to SNP...

We consider the problem of ranking a set of OT constraints in a manner consistent with data. (1) We speed up Tesar and Smolensky’s RCD algorithm to be linear on the number of constraints. This finds a ranking so each attested form xi beats or ties a particular competitor yi. (2) We also generalize RCD so each xi beats or ties all possible competitors. Alas, neither ranking as in (2) nor even ge...

A permutation π contains a permutation σ as a pattern if it contains a subsequence of length |σ| whose elements are in the same relative order as in the permutation σ. This notion plays a major role in enumerative combinatorics. We prove that the problem does not have a polynomial kernel (under the widely believed complexity assumption NP 6⊆ co-NP/poly) by introducing a new polynomial reduction...

We consider the problem of ranking a set of OT constraints in a manner consistent with data. (1) We speed up Tesar and Smolensky’s RCD algorithm to be linear on the number of constraints. This finds a ranking so each attested form xi beats or ties a particular competitor yi. (2) We also generalize RCD so each xi beats or ties all possible competitors. Alas, neither ranking as in (2) nor even ge...

Bodlaender et al.’s [SIDMA 2014] cross-composition technique is a popular method for excluding polynomial-size problem kernels for NP-hard parameterized problems. We present a new technique exploiting triangle-based fractal structures for extending the range of applicability of cross-compositions. Our technique makes it possible to prove new no-polynomial-kernel results for a number of problems...