Journal of the ACM (JACM) - The MIT Press scientific computation series
On verifying that a concurrent program satisfies a nondeterministic specification
Information Processing Letters
Handbook of theoretical computer science (vol. B)
Theoretical Computer Science
Proof systems for infinite behaviours
Information and Computation
Taking it to the limit: on infinite variants of NP-complete problems
Journal of Computer and System Sciences
Handbook of formal languages, vol. 3
Handbook of formal languages, vol. 3
Recurring Dominoes: Making the Highly Undecidable Highly Understandable (Preliminary Report)
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Logical Specifications of Infinite Computations
A Decade of Concurrency, Reflections and Perspectives, REX School/Symposium
Borel hierarchy and omega context free languages
Theoretical Computer Science
Tiling systems over infinite pictures and their acceptance conditions
DLT'02 Proceedings of the 6th international conference on Developments in language theory
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Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the Büchi andMuller ones, in [1]. It was proved in [9] that it is undecidable whether a Büchirecognizable language of infinite pictures is E-recognizable (respectively, A-recognizable). We show here that these two decision problems are actually П$^{1}_{2}$-complete, hence located at the second level of the analytical hierarchy, and "highly undecidable". We give the exact degree of numerous other undecidable problems for Büchi-recognizable languages of infinite pictures. In particular, the nonemptiness and the infiniteness problems are Σ$^{1}_{1}$-complete, and the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, are all П$^{1}_{2}$-complete. It is also П$^{1}_{2}$-complete to determine whether a given Büchi recognizable language of infinite pictures can be accepted row by row using an automaton model over ordinal words of length ω$^{2}$.