Unified Analysis of Collapsible and Ordered Pushdown Automata via Term Rewriting

We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term rewriting systems, which is obtained by extending the classic saturation-based approach. This result subsumes and unifies similar analyses on collapsible and ordered pushdown systems. Despite the rich literature on inverse preservation of recognizability for term rewrite systems, our result does not seem to follow from any previous study.Comment: in Proc. of FRE

Automating the First-Order Theory of Rewriting for Left-Linear Right-Ground Rewrite Systems

The first-order theory of rewriting is decidable for finite left-linear right-ground rewrite systems. We present a new tool that implements the decision procedure for this theory. It is based on tree automata techniques. The tool offers the possibility to synthesize rewrite systems that satisfy properties that are expressible in the first-order theory of rewriting

Leftmost Outermost Revisited

We present an elementary proof of the classical result that the leftmost outermost strategy is normalizing for left-normal orthogonal rewrite systems. Our proof is local and extends to hyper-normalization and weakly orthogonal systems. Based on the new proof, we study basic normalization, i.e., we study normalization if the set of considered starting terms is restricted to basic terms. This allows us to weaken the left-normality restriction. We show that the leftmost outermost strategy is hyper-normalizing for basically left-normal orthogonal rewrite systems. This shift of focus greatly extends the applicability of the classical result, as evidenced by the experimental data provided

Sequentiality, Monadic Second-Order Logic and Tree Automata

Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal form, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.-J. Lévy define in [9] the sequentiality of a predicate P on partially evaluated terms. We show here that the sequentiality of P is definable in SkS, the monadic second-order logic with k successors, provided P is definable in SkS. We derive several known an new consequences of this remark: 1-strong sequentiality, as defined in [9], of a left linear (possibly overlapping) rewrite system is decidable, 2-NV-sequentiality, as defined in [17] is decidable, even in the case of overlapping rewrite systems 3-sequentiality of any linear shallow rewrite system is decidable. Then we describe a direct construction of a tree automaton recognizing the set of terms that do have needed redexes, whi..

Bohm-Like Trees for Rewriting

Klop, J.W. [Promotor]Raamsdonk, F. [Copromotor]Vrijer, R.C. de [Copromotor