In this talk we are going to explore an interesting connection between the famous Burnside problem for groups, regular languages, and residuated lattices. Let K be a finitely axiomatized class of residuated lattices. Recall that the usual way of proving decidability of universal theory for K is to establish that K has the finite embeddability property (FEP) [2, 3]. It turns out that the method ...

These lecture notes contain all material relevant for the examinations and the course. For further reading, the author refers to the textbooks Automata Theory and its Applications by Bakhadyr Khoussainov and Anil Nerode [46] and Introduction to Automata Theory, Languages, and Computation by Hopcroft, Motwani and Ullman [35]. The author would like to thank Volker Diekert, Henning Fernau, Vladimi...

Intuitionistic logic is an important variant of classical logic, but it is not as well-understood, even in the propositional case. In this thesis, we describe a faithful representation of intuitionistic propositional formulas as tree automata. This representation permits a number of consequences, including a characterization theorem for free Heyting algebras, which are the intutionistic analogu...

Randomizing reductions have provided new techniques for tackling average-case complexity problems. For example, although some NP-complete problems with uniform distributions on instances cannot be complete under deterministic one-one reductions [WB95], they are complete under randomized reductions [VL88]. We study randomized reductions in this paper on reductions that are one-one and honest map...

It is known that injective Cellular Automata (CA) are surjective. In general, the converse is not true, and there are many algebraic CA counterexamples. However, there are interesting subclasses where this might be true. For example, if a surjective CA has entropy 0 then it is almost injective (Moothathu (2011)) and it is not known if it is actually injective. The author believes there are some...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

Hybrid systems are interacting systems of digital automata and continuous plants subject to disturbances. The digital automata are used to force the state trajectory of the continuous plant to obey a performance specification. For the basic concepts and notation for hybrid systems, see Kohn and Nerode (1993), and other papers in the same volume. Here we introduce tools for analyzing enforcing v...

Nerode et al. [ 131 showed that a correct concurrent program can be viewed as a winning strategy in a suitably defined two player game played between the Programmer and the Computer in which the program specification is defined by the rules of the game together with the winning condition. This gives rise to the question as to whether there are useful algorithms to extract (provably) winning str...