Abstract
Context-free games on strings are two-player rewriting games based on a set of production rules and a regular target language. In each round, the first player selects a position of the current string; then the second player replaces the symbol at that position according to one of the production rules. The first player wins as soon as the current string belongs to the target language. In this paper the one-pass setting for context-free games is studied, where the knowledge of the first player is incomplete: She selects positions in a left-to-right fashion and only sees the current symbol and the symbols from previous rounds. The paper studies conditions under which dominant and undominated strategies exist for the first player, and when they can be chosen from restricted types of strategies that can be computed efficiently.
The first author is supported by EPSRC Award 1652110.
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Notes
- 1.
The restriction to strings instead of trees was justified in [11].
- 2.
In [3], dominant and undominated strategies were called optimum and optimal respectively.
- 3.
As explained later, every game can be transformed into a very similar prefix-free game.
- 4.
The assumption that T is minimal will be convenient at times.
- 5.
We usually omit brackets and write, e.g., \(\natural \alpha \beta \) for \(\natural (\alpha \beta )\).
- 6.
Even though we think of Romeo as an omniscient adversary, it is not necessary to provide the remaining string as an argument to \(\tau \): The remaining string is uniquely determined by the input word and his own and Juliet’s previous moves.
- 7.
Since the \(\rho _k\) are only partially defined, one might consider the strategies \(\sigma _k\) that result from the \(\rho _k\) which take the value \( Call \) whenever \(\rho _k\) is undefined.
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Coester, C., Schwentick, T., Schuster, M. (2019). Winning Strategies for Streaming Rewriting Games. In: Gąsieniec, L., Jansson, J., Levcopoulos, C. (eds) Fundamentals of Computation Theory. FCT 2019. Lecture Notes in Computer Science(), vol 11651. Springer, Cham. https://doi.org/10.1007/978-3-030-25027-0_4
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