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International audience; This special issue contains eight articles which are based on extended abstracts that were presented at the 35th Symposium on Theoretical Aspects of Computer Science (STACS), which was held at the University of Caen from February 28th to March 3rd, 2018. These extended abstracts were chosen among the top papers of those that were selected for presentation at STACS 2018 in a highly competitive peer-review process (after which only 54 papers out of 186 submissions were accepted). Compared with the original extended abstracts, the articles have been extended with a description of the context, full proofs and additional results. They underwent a further rigorous reviewing process, following the TOCS Journal standards, completely independent from the selection process of STACS 2018. The topics of the chosen papers cover a rich set of areas within Theoretical Computer Science, that is, algorithmic game theory, automata theory, circuit complexity, efficient algorithms, logic and model checking, Markov chains, pa-rameterized complexity, and proof complexity. Kernelization (provably effective and efficient preprocessing) is a central theme in parameterized complexity. The article Computing Hitting Set Kernels by AC 0-Circuits by Max Bannach and Till Tantau presents for the first time kernels for the d-Hitting Set problem that can be computed in constant parallel time, thereby refuting a previous conjecture. To this end, the authors introduce a new, generalized notion of hypergraph sunflowers. Altogether, this gives an important contribution to parameterized circuit complexity.

The Parikh automaton model equips a finite automaton with integer registers and imposes a semilinear constraint on the set of their final settings. Here the theories of typed monoids and of rational series are used to characterize the language classes that arise algebraically. Complexity bounds are derived, such as containment of the unambiguous Parikh automata languages in NC1. Affine Parikh automata, where each transition applies an affine transformation on the registers, are also considered. Relying on these characterizations, the landscape of relationships and closure properties of the classes at hand is completed, in particular over unary languages.