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- Naohi Eguchi
- ArXiv
- 2009

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)

- Martin Avanzini, Naohi Eguchi, Georg Moser
- Theor. Comput. Sci.
- 2012

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 system… (More)

- Toshiyasu Arai, Naohi Eguchi
- ACM Trans. Comput. Log.
- 2009

Bellantoni and Cook have given a function-algebra characterization of the polynomial-time computable functions via an unbounded recursion scheme which is called safe recursion. Inspired by their work, we characterize the exponential-time computable functions with the use of a safe variant of nested recursion.

- Martin Avanzini, Naohi Eguchi, Georg Moser
- RTA
- 2011

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)

- Naohi Eguchi
- Math. Log. Q.
- 2009

- Naohi Eguchi
- ArXiv
- 2013

The predicative lexicographic path order (PLPO for short), a syntactic restriction of the lexicographic 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)

- Naohi Eguchi
- ArXiv
- 2014

In this paper we present a new termination proof and complexity analysis of unfolding graph rewriting which is a specific kind of infinite graph rewriting expressing the general form of safe recursion. We introduce a termination order over sequences of terms together with an interpretation of term graphs into sequences of terms. Unfolding graph rewrite… (More)

- Martin Avanzini, Naohi Eguchi, Georg Moser
- ArXiv
- 2010

In this paper we present a new path order for rewrite systems, the exponential path order EPO ⋆. Suppose a term rewrite system R is compatible with EPO ⋆ , then the runtime complexity of R is bounded from above by an exponential function. Further, the class of function computed by a rewrite system compatible with EPO ⋆ equals the class of functions… (More)

- Naohi Eguchi
- FICS
- 2015

It is known that (i) programs can be executed in polynomial space if they are compatible with lexicographic path orders (LPOs) and admit polynomial quasi-interpretations (PQIs), and (ii) LPO-termination proofs can be formalized in the Σ2-induction fragment of Peano arithmetic. We show that LPO-termination proofs can be formalized in the second order system… (More)

- Naohi Eguchi
- TERMGRAPH
- 2014

The general form of safe recursion (or ramified recurrence) can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which the size of every normal form by innermost rewriting is polynomially bounded. Every unfolding graph rewrite rule is precedence terminating in the sense of… (More)