683,856 research outputs found

    Rigorous computer analysis of the Chow-Robbins game

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    Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded number crunching can show that it is best to continue in a given position, establishing rigorously that stopping is optimal seems at first sight to require "backward induction from infinity". We establish a simple upper bound on the expected payoff in a given position, allowing efficient and rigorous computer analysis of positions early in the game. In particular we confirm that with 5 heads and 3 tails, stopping is optimal.Comment: 10 page

    Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

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    Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature
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