1,726 research outputs found
Termination Proofs for Logic Programs with Tabling
Tabled logic programming is receiving increasing attention in the Logic
Programming community. It avoids many of the shortcomings of SLD execution and
provides a more flexible and often extremely efficient execution mechanism for
logic programs. In particular, tabled execution of logic programs terminates
more often than execution based on SLD-resolution. In this article, we
introduce two notions of universal termination of logic programming with
Tabling: quasi-termination and (the stronger notion of) LG-termination. We
present sufficient conditions for these two notions of termination, namely
quasi-acceptability and LG-acceptability, and we show that these conditions are
also necessary in case the tabling is well-chosen. Starting from these
conditions, we give modular termination proofs, i.e., proofs capable of
combining termination proofs of separate programs to obtain termination proofs
of combined programs. Finally, in the presence of mode information, we state
sufficient conditions which form the basis for automatically proving
termination in a constraint-based way.Comment: 48 pages, 6 figures, submitted to ACM Transactions on Computational
Logic (TOCL
Polynomial Path Orders: A Maximal Model
This paper is concerned with the automated complexity analysis of term
rewrite systems (TRSs for short) and the ramification of these in implicit
computational complexity theory (ICC for short). We introduce a novel path
order with multiset status, the polynomial path order POP*. Essentially relying
on the principle of predicative recursion as proposed by Bellantoni and Cook,
its distinct feature is the tight control of resources on compatible TRSs: The
(innermost) runtime complexity of compatible TRSs is polynomially bounded. We
have implemented the technique, as underpinned by our experimental evidence our
approach to the automated runtime complexity analysis is not only feasible, but
compared to existing methods incredibly fast. As an application in the context
of ICC we provide an order-theoretic characterisation of the polytime
computable functions. To be precise, the polytime computable functions are
exactly the functions computable by an orthogonal constructor TRS compatible
with POP*
Productive Corecursion in Logic Programming
Logic Programming is a Turing complete language. As a consequence, designing
algorithms that decide termination and non-termination of programs or decide
inductive/coinductive soundness of formulae is a challenging task. For example,
the existing state-of-the-art algorithms can only semi-decide coinductive
soundness of queries in logic programming for regular formulae. Another, less
famous, but equally fundamental and important undecidable property is
productivity. If a derivation is infinite and coinductively sound, we may ask
whether the computed answer it determines actually computes an infinite
formula. If it does, the infinite computation is productive. This intuition was
first expressed under the name of computations at infinity in the 80s. In
modern days of the Internet and stream processing, its importance lies in
connection to infinite data structure processing.
Recently, an algorithm was presented that semi-decides a weaker property --
of productivity of logic programs. A logic program is productive if it can give
rise to productive derivations. In this paper we strengthen these recent
results. We propose a method that semi-decides productivity of individual
derivations for regular formulae. Thus we at last give an algorithmic
counterpart to the notion of productivity of derivations in logic programming.
This is the first algorithmic solution to the problem since it was raised more
than 30 years ago. We also present an implementation of this algorithm.Comment: Paper presented at the 33nd International Conference on Logic
Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017
16 pages, LaTeX, no figure
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