Abstract
Infinite games are studied in a format where two players, called Player 1 and Player 2, generate a play by building up an ω-word as they choose letters in turn. A game is specified by the ω-language which contains the plays won by Player 2. We analyze ω-languages generated from certain classes \({\cal K}\) of regular languages of finite words (called *-languages), using natural transformations of *-languages into ω-languages. Winning strategies for infinite games can be represented again in terms of *-languages. Continuing work of Selivanov (2007) and Rabinovich et al. (2007), we analyze how these “strategy *-languages” are related to the original language class \({\cal K}\). In contrast to that work, we exhibit classes \({\cal K}\) where strategy representations strictly exceed \({\cal K}\).
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Chaturvedi, N., Olschewski, J., Thomas, W. (2011). Languages vs. ω-Languages in Regular Infinite Games. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_16
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DOI: https://doi.org/10.1007/978-3-642-22321-1_16
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