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Institute of Computer Science

The Czech Academy of Sciences

The Czech Academy of Sciences

"The problems of the real world are primarily those you are left with when you refuse to apply their effective solutions." - E. W. Dijkstra

Members of our department are focused on the more foundational aspects of Theoretical Computer Science and their work can be classified into three main areas: *Combinatorics, Computational Complexity, and Mathematical Logic. *In all these areas, we strive not only to achieve new results but to broaden the repertoire of approaches that are considered standard. In particular we pursue three main aims:

*Combinatorics: *to study the recent challenging problems of extremal graph theory and discrete random structures, and thus contribute to these central topics in combinatorics which are crucial e.g. for our understating of very large networks.

*Computational Complexity: *to deepen our knowledge of relations among complexity classes via standard and non-standard computational models considering both the usual complexity measures like time or space and new ones relevant in neurocomputing and knowledge compilation.

*Mathematical* *Logic: *to develop and apply non-classical logics for reasoning, in both natural and artificial scenarios, with real-life information, which is often uncertain, graded, or even contradictory, and changing over time.

*Combinatorics: *Extremal Graph Theory, Regularity Method, Probabilistic Method, Limits of Graphs, Random Graphs, Discrete Structures, Computational Geometry, Combinatorial and Algebraic Methods in Number Theory.

*Computational Complexity:* Branching Programs, Neural Networks, Boolean Functions, Preprocessing Instances for SAT Problem, Knowledge Compilation, Logical Descriptions of Computation, Non-Standard Positional Numeral Systems.

*Mathematical **Logic*: Logic and Reasoning, Graded Notions, Vagueness, Uncertainty, Mathematical Fuzzy Logic, Substructural Logics, Paraconsistent Logic, Dynamic and Non-Monotonic Logic, Modal Logic, Abstract Algebraic Logic, Complexity of Non-Classical Logics.

Combinatorial group: a group dedicated to study of extremal graph theory, discrete structures, and computational geometry. In collaboration with the group Graph limits and inhomogeneous random graphs from the Institute of Mathematics of the Czech Academy of Sciences we organize a combinatorial seminar .

LogICS: a group dedicated to study of (non-classical) logic. Together with the Czech Society for Cybernetics and Informatics we organize a seminar on applied mathematical logic (also called Hájek’s seminar according to its founder) which has run continuously since the late 1960’s.

- FoNeCo: Analytical Foundations of Neurocomputing (2019-2021; GAČR)
- National Competence Center – Cybernetics and Artificial Intelligence (2019-2021; GAČR)
- Boolean Representation Languages Complete for Unit Propagation (2019-2021; GAČR)
- Structural properties of visibility in terrains and farthest color Voronoi diagrams (2019-2021; GAČR)
- Embedding, Packing and Limits in Graphs (2019-2021; GAČR)
- Enhancing human resources for research in theoretical computer science (2018-2020; MŠMT)
- Non-classical Logical Models of Information Dynamics (2018-2020; GAČR)
- Reasoning with Graded Properties (2018-2020; GAČR)
- CONNECT – Combinatorics of Networks and Computation (2017-2020; H2020 MSCA RISE)
- Predicate graded logics and their applications to computer science 2017-2019; GAČR)
- SYSMICS: Syntax meets semantics: Methods, interactions, and connections in substructural logics (2016-2019; GAČR)
- Extremal graph theory and applications (2016-2018; GAČR)
- Modelling vague quantifiers in mathematical fuzzy logic (2015-2017; GAČR)
- An Order-Based Approach to Non-Classical Propositional and Predicate Logics (2013-2016; GAČR)
- Center of Excellence – Institute for Theoretical Computer Science (2012-2018; GAČR)
- Distribution and metric properties of number sequences and their applications (2012-2015; GAČR)
- Algebraic Methods in Proof Theory (2011-2015; GAČR)

- Kučera Petr;
**Savický Petr**; Vorel Vojtěch. A lower bound on CNF encodings of the at-most-one constraint. Theoretical Computer Science, 2018 **Šíma Jiří; Savický Petr**. Quasi-periodic β – expansions and cut languages. Theoretical Computer Science, 2018- Bezhanishvili Guram;
**Moraschini Tommaso**; Raftery James Gordon. Epimorphisms in Varieties of Residuated Structures. Journal of Algebra, 2017 - Cabello Sergio; Cibulka Josef; Kynčl Jan;
**Saumell Maria**; Valtr Pavel. Peeling Potatoes Near-Optimally in Near-Linear Time. SIAM Journal on Computing, 2017 **Moraschini Tommaso**. A Computational Glimpse at the Leibniz and Frege Hierarchies. Annals of Pure and Applied Logic, 2017**Šíma Jiří; Žák Stanislav**. On tight separation for Blum measures applied to Turing machine buffer complexity. Fundamenta Informaticae, 2017- Böttcher Julia; Hladký Jan;
**Piguet Diana**; Taraz Anusch. An approximate version of the tree packing conjecture. Israel Journal of Mathematics, 2016 **Haniková Zuzana; Savický Petr**. Term satisfiability in FLew-algebras. Theoretical Computer Science 31, 2016- Hladký Jan;
**Piguet Diana**; Simonovits Miklos; Stein Maya; Szemeredi Endre. The approximate Loebl-Komlos-Sos conjecture and embedding trees in sparse graphs. Electronic Research Announcements in Mathematical Sciences, 2016 - Hladký Jan;
**Piguet Diana**. Loebl-Komlos-Sos Conjecture: dense case. Journal of Combinatorial Theory, 2016 **Chvalovský Karel; Horčík Rostislav**. Full Lambek Calculus with Contraction is Undecidable. Journal of Symbolic Logic, 2016**Moraschini Tommaso**. The Semantic Isomorphism Theorem in Abstract Algebraic Logic. Annals of Pure and Applied Logic, 2016- Strauch Oto;
**Porubský Štefan**. Distribution of Sequences: A Sampler. Peter Lang GmbH, Electronic revised version December 8, 2016 **Cintula Petr**(ed.); Fermüller C. (ed.);**Hájek Petr**(ed.), Noguera Carles (ed.). Handbook of Mathematical Fuzzy Logic (in three volumes). London: College Publications, 2011, 2015**Cintula Petr**; Noguera Carles. A Henkin-Style Proof of Completeness for First-Order Algebraizable Logics. Journal of Symbolic Logic, 2015**Chvalovský Karel**. Undecidability of consequence relation in Full Non-associative Lambek Calculus. Journal of Symbolic Logic, 2015**Horčík Rostislav**. Word Problem for Knotted Residuated Lattices. Journal of Pure and applied Algebra, 2015

- Prague Gathering of Logicians and Beauty of Logic 2018
- 23rd Czech and Slovak International Conference on Number Theory 2017
- Topology, Algebra, and Categories in Logic 2017
- Non-classical Modal and Predicate Logics 2017
- Prague seminar: The Future of Mathematical Fuzzy Logic 2016
- Prague Gathering of Logicians 2015
- Prague seminar on Non-Classical Mathematics 2015
- 4th International Conference on Uniform Distribution Theory 2014
- Prague Seminar on Substructural Logics 2014
- 2nd Prague Symposium on Semilinear Logics 2013
- 21st Czech and Slovak International Conference on Number Theory 2013
- Gathering of Prague-Based Logicians 2013
- Manyval 2013
- ALANT Joint Conferences on Algebra, Logic and Number Theory 2012
- 20th Czech and Slovak International Conference on Number Theory 2011
- Logic, Algebra and Truth Degrees 2010
- 19th Czech and Slovak International Conference on Number Theory 2009
- 9th Central European Conference on Cryptography 2009
- 5th Polish, Slovak and Czech Conference on Number Theory 2004

- Ankush Acharyya
- Marta Bílková
- Zuzana Haniková
- Ramesh Kumar Jallu
- Vahideh Keikha
- Ondrej Majer
- Eva Martinčíková
- Diana Piguet
- Štefan Porubský
- Vít Punčochář
- Jakub Rozlivek
- Hanka Řada
- Nicolás Sanhueza
- Maria Saumell Mendiola
- Petr Savický
- Igor Sedlár
- Matas Šileikis
- Jiří Šíma
- Andrew Tedder
- Stanislav Žák

**Head: **Petr Cintula

**Secretarial support: **Iveta Kubíková