We introduce a type of isomorphism among strategic games that we call local isomorphism. Local isomorphisms is a weaker version of the notions of strong and weak game isomorphism introduced in [J. Gabarro, A. Garcia and M. Serna, Theor. Comput. Sci. 412 (2011) 6675-6695]. In a local isomorphism it is required to preserve, for any player, the player's preferences on the sets of strategy profiles that differ only in the action selected by this player. We show that the game isomorphism problem for local isomorphism is equivalent to the same problem for strong or weak isomorphism for strategic games given in: general, extensive and formula general form. As a consequence of the results in [J. Gabarro, A. Garcia and M. Serna, Theor. Comput. Sci. 412 (2011) 6675-6695] this implies that local isomorphism problem for strategic games is equivalent to (a) the circuit isomorphism problem for games given in general form, (b) the boolean formula isomorphism problem for formula games in general form, and (c) the graph isomorphism problem for games given in explicit form
This paper studies the computational complexity of the proper interval colored graph problem (picg), when the input graph
is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the picg and a graph layout problem the proper colored layout problem (pclp). We show a dichotomy: the picg and the pclp are NP-complete for colored caterpillars of hair length ≥2, while both problems are in P for colored caterpillars of hair length <2. For the hardness results we provide a reduction from the multiprocessor scheduling problem, while the polynomial time results follow from a characterization in terms of forbidden
Proves that nonprimitive recursive functions have transcendental generating series. This result translates a certain measure of the complexity of a function, the fact of not being primitive recursive, into another measure of the complexity of the generating series associated to the function, the fact of being transcendental.
We characterize in terms of oracle Turing machines the classes defined by exponential lower bounds on some nonuniform complexity measures. After, we use the same methods to giue a new characterization of classes defined by polynomial and polylog upper bounds, obtaining an unified approach to deal with upper and lower bounds, The main measures are the initial index, the context-free cosU ond the boolean circuits size. We interpret our results by discussing a trade- off between oracle information and computed information for oracle Turing machines.
The existence of immune and simple sets in relativizations of the probabilistic polynomial time bounded classes is studied. Some techniques previously used to show similar results for relativizations of P and NP are adapted to the probabilistic classes. Using these results, an exhaustive settling of ail possible strong séparations among these relativized classes is obtained.