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Thirdorder computation and bounded arithmetic
 University of Wales Swansea
, 2006
"... Abstract. We describe a natural generalization of ordinary computation to a thirdorder setting and give a function calculus with nice properties and recursiontheoretic characterizations of several large complexity classes. We then present a number of thirdorder theories of bounded arithmetic whos ..."
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Abstract. We describe a natural generalization of ordinary computation to a thirdorder setting and give a function calculus with nice properties and recursiontheoretic characterizations of several large complexity classes. We then present a number of thirdorder theories of bounded arithmetic whose definable functions are the classes of the EXPtime hierarchy in the thirdorder setting.