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Isabel Oitavem has introduced a term rewriting system (TRS) which captures the class FPS of polynomial-space computable functions. We propose an alternative TRS for FPS. As a consequence, it is obtained that FPS is the smallest class containing certain initial functions and closed under specific operations. It turns out that our characterization is(More)
We propose a new order, the small polynomial path order (sPOP * for short). The order sPOP * provides a characterisation of the class of polynomial time computable function via term rewrite systems. Any polynomial time computable function gives rise to a rewrite system that is compatible with sPOP *. On the other hand any function defined by a rewrite(More)
In this paper we present a new path order for rewrite systems, the exponential path order EPO. Suppose a term rewrite system is compatible with EPO , then the runtime complexity of this rewrite system is bounded from above by an exponential function. Furthermore, the class of function computed by a rewrite system compatible with EPO equals the class of(More)
The predicative lexicographic path order (PLPO for short), a syntactic restriction of the lex-icographic path order, is presented. As well as lexicographic path orders, several non-trivial primitive recursive equations, e.g., primitive recursion with parameter substitution, unnested multiple recursion, or simple nested recursion, can be oriented with PLPOs.(More)
In this paper we present a novel termination order the pred-icative lexicographic path order (PLPO for short), a syntactic restriction of the lexicographic path order. As well as lexicographic path orders, several non-trivial primitive recursive equations, e.g., primitive recur-sion with parameter substitution, unnested multiple recursion, or simple nested(More)
In this talk we will discuss about proof-theoretic approaches to computational complexity in terms of weak theories of arithmetic as known as theories of bounded arithmetic, which was initiated by Samuel Buss. We will start with classical facts on primitive recursive functions, and then go into discussion about polynomial time functions and polynomial space(More)