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- Faried Abu Zaid, Erich Grädel, Martin Grohe, Wied Pakusa
- MFCS
- 2014

Choiceless Polynomial Time (CPT) is one of the candidates in the quest for a logic for polynomial time. It is a strict extension of fixed-point logic with counting (FPC) but to date it is unknown whether it expresses all polynomial-time properties of finite structures. We study the CPT-definability of the isomorphism problem for relational structures of… (More)

- Anuj Dawar, Erich Grädel, Bjarki Holm, Eryk Kopczynski, Wied Pakusa
- CSL
- 2012

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 rings from the viewpoint of logical (inter-)definability. All problems that we consider are decidable in polynomial… (More)

- Faried Abu Zaid, Erich Grädel, Lukasz Kaiser, Wied Pakusa
- Theory of Computing Systems
- 2013

We investigate structural properties of ω-automatic presentations of infinite structures in order to sharpen our methods to determine whether a given structure is ω-automatic. We apply these methods to show that several classes of structures such as pairing functions and infinite integral domains do not have an ω-automatic model.

- Erich Grädel, Wied Pakusa
- CSL
- 2015

Motivated by the search for a logic for polynomial time, we study rank logic (FPR) which extends fixed-point logic with counting (FPC) by operators that determine the rank of matrices over finite fields. While FPR can express most of the known queries that separate FPC from Ptime, nearly nothing was known about the limitations of its expressive power. In… (More)

- Faried Abu Zaid, Anuj Dawar, Erich Grädel, Wied Pakusa
- 2017 32nd Annual ACM/IEEE Symposium on Logic in…
- 2017

We study the descriptive complexity of summation problems in Abelian groups and semigroups. In general, an input to the summation problem consists of an Abelian semigroup G, explicitly represented by its multiplication table, and a subset X of G. The task is to determine the sum over all elements of X.

- Martin Grohe, Wied Pakusa
- 2017 32nd Annual ACM/IEEE Symposium on Logic in…
- 2017

We prove that the solvability of systems of linear equations and related linear algebraic properties are definable in a fragment of fixed-point logic with counting that only allows polylogarithmically many iterations of the fixed-point operators. This enables us to separate the descriptive complexity of solving linear equations from full fixed-point logic… (More)

- Erich Grädel, Wied Pakusa, Svenja Schalthöfer, Lukasz Kaiser
- 2015 30th Annual ACM/IEEE Symposium on Logic in…
- 2015

Choice less Polynomial Time (CPT) is one of the candidates in the quest for a logic for polynomial time. It is a strict extension of fixed-point logic with counting, but to date the question is open whether it expresses all polynomial-time properties of finite structures. We present here alternative characterisations of Choice less Polynomial Time (with and… (More)

- Felix Canavoi, Erich Grädel, Simon Leßenich, Wied Pakusa
- 2015 30th Annual ACM/IEEE Symposium on Logic in…
- 2015

We study definability questions for positional winning strategies in infinite games on graphs. The quest for efficient algorithmic constructions of winning regions and winning strategies in infinite games, in particular parity games, is of importance in many branches of logic and computer science. A closely related, yet different, facet of this problem… (More)

- Wied Pakusa, Svenja Schalthöfer, Erkal Selman
- CSL
- 2016

Choiceless Polynomial Time (CPT) is one of the most promising candidates in the search for a logic capturing Ptime. The question whether there is a logic that expresses exactly the polynomial-time computable properties of finite structures, which has been open for more than 30 years, is one of the most important and challenging problems in finite model… (More)