Abstract
We prove an applicative characterization of poly-space as the set of functions over \(\mathbb{W} = \{ 0,1\} *\)defined by ramified \(\mathbb{W}\)-recurrence with parameter substitution. Intuitively, parameter substitution allows re-use of space in ways disallowed by ramified recurrence without substitution: it permits capturing by recurrence the flow of computation backwards from accepting configurations, thereby enabling the simulation of parallel (alternating) computing. Conversely, parameter substitution can be simulated by a computation that can repeatedly bifurcate into subcomputations, i.e. by parallelism that can be captured in poly-space.
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Leivant, D., Marion, JY. (1995). Ramified recurrence and computational complexity II: Substitution and poly-space. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022277
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DOI: https://doi.org/10.1007/BFb0022277
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