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We present a notion of logspace reducibility among structures that is based on abstract state machines (ASM). Our reductions are logspace computable (due to the syntactic restrictions we impose on ASM-programs) and are equally expressive as the logic (FO+DTC) enriched with the ability to handle sets. On ordered structures they precisely capture Logspace. Our work continues that of Blass, Gurevich and Shelah on the choiceless fragment of Ptime. Indeed, our reductions can be seen as the choiceless fragment of Logspace.

Logspace reducibility via abstract state machines