NDLI: Collapsible Pushdown Automata and Recursion Schemes

Content Provider	IEEE Xplore Digital Library
Author	Hague, M. Murawski, A.S. Ong, C.-H.L. Serre, O.
Copyright Year	2008
Description	Author affiliation: Comput. Lab., Oxford Univ., Oxford (Hague, M.)
Abstract	Collapsible pushdown automata (CPDA) are a new kind of higher-order pushdown automata in which every symbol in the stack has a link to a stack situated somewhere below it. In addition to the higher-order push and pop operations, CPDA have an important operation called collapse, whose effect is to "collapse" a stack s to the prefix as indicated by the link from the topmost symbol of s. Our first result is that CPDA are equi-expressive with recursion schemes as generators of (possibly infinite) ranked trees. In one direction, we give a simple algorithm that transforms an order-n CPDA to an order-n recursion scheme that generates the same tree, uniformly for all n Gt= 0. In the other direction, using ideas from game semantics, we give an effective transformation of order-n recursion schemes (not assumed to be homogeneously typed, and hence not necessarily safe) to order-n CPDA that compute traversals over an abstract syntax graph of the scheme, and hence paths in the tree generated by the scheme. Our equi-expressivity result is the first automata-theoretic characterization of higher-order recursion schemes. Thus CPDA are also a characterization of the simply-typed lambda calculus with recursion (generated from uninterpreted 1st-order symbols) and of (pure) innocent strategies. An important consequence of the equi-expressivity result is that it allows us to reduce decision problems on trees generated by recursion schemes to equivalent problems on CPDA and vice versa. Thus we show, as a consequence of a recent result by Ong (modal mu-calculus model-checking of trees generated by recursion schemes is n-EXPTIME complete), that the problem of solving parity games over the configuration graphs of order-n CPDA is n-EXPTIME complete, subsuming several well-known results about the solvability of games over higher-order pushdown graphs by (respectively) Walukiewicz, Cachat, and Knapik et al. Another contribution of our work is a self-contained proof of the same solvability result by generalizing standard techniques in the field. By appealing to our equi-expressivity result, we obtain a new proof of Ong's result. In contrast to higher-order pushdown graphs, we show that the monadic second-order theories of the configuration graphs of CPDA are undecidable. It follows that -- as generators of graphs -- CPDA are strictly more expressive than higher-order pushdown automata.
Starting Page	452
Ending Page	461
File Size	317893
Page Count	10
File Format	PDF
ISBN	9780769531830
ISSN	10436871
DOI	10.1109/LICS.2008.34
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-06-24
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Automata Tree graphs Personal digital assistants Character generation Logic Computer science Calculus Laboratories Safety game semantics Higher-order pushdown automata higher-order recursion schemes
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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