455 research outputs found
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
Acceptability with general orderings
We present a new approach to termination analysis of logic programs. The
essence of the approach is that we make use of general orderings (instead of
level mappings), like it is done in transformational approaches to logic
program termination analysis, but we apply these orderings directly to the
logic program and not to the term-rewrite system obtained through some
transformation. We define some variants of acceptability, based on general
orderings, and show how they are equivalent to LD-termination. We develop a
demand driven, constraint-based approach to verify these
acceptability-variants.
The advantage of the approach over standard acceptability is that in some
cases, where complex level mappings are needed, fairly simple orderings may be
easily generated. The advantage over transformational approaches is that it
avoids the transformation step all together.
{\bf Keywords:} termination analysis, acceptability, orderings.Comment: To appear in "Computational Logic: From Logic Programming into the
Future
Observation of implicit complexity by non confluence
We propose to consider non confluence with respect to implicit complexity. We
come back to some well known classes of first-order functional program, for
which we have a characterization of their intentional properties, namely the
class of cons-free programs, the class of programs with an interpretation, and
the class of programs with a quasi-interpretation together with a termination
proof by the product path ordering. They all correspond to PTIME. We prove that
adding non confluence to the rules leads to respectively PTIME, NPTIME and
PSPACE. Our thesis is that the separation of the classes is actually a witness
of the intentional properties of the initial classes of programs
Analysis of Probabilistic Basic Parallel Processes
Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They
are the simplest common model of concurrent programs that allows unbounded
spawning of processes. In the probabilistic version of BPPs, every process
generates other processes according to a probability distribution. We study the
decidability and complexity of fundamental qualitative problems over
probabilistic BPPs -- in particular reachability with probability 1 of
different classes of target sets (e.g. upward-closed sets). Our results concern
both the Markov-chain model, where processes are scheduled randomly, and the
MDP model, where processes are picked by a scheduler.Comment: This is the technical report for a FoSSaCS'14 pape
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Discrete Feature Approach for Heterogeneous Reservoir Production Enhancement
This progress report describes activities during the period January 1, 1999 to June 30, 1999. Work was carried out on 21 tasks. The major activity during the reporting period was the development and preliminary application of discrete fracture network (DFN) models for Stoney Point, South Oregon Basin, and North Oregon Basins project study sites. In addition, research was carried out on analysis algorithms for discrete future orientation
Lazy AC-Pattern Matching for Rewriting
We define a lazy pattern-matching mechanism modulo associativity and
commutativity. The solutions of a pattern-matching problem are stored in a lazy
list composed of a first substitution at the head and a non-evaluated object
that encodes the remaining computations. We integrate the lazy AC-matching in a
strategy language: rewriting rule and strategy application produce a lazy list
of terms.Comment: In Proceedings WRS 2011, arXiv:1204.531
Soundness of Unravelings for Conditional Term Rewriting Systems via Ultra-Properties Related to Linearity
Unravelings are transformations from a conditional term rewriting system
(CTRS, for short) over an original signature into an unconditional term
rewriting systems (TRS, for short) over an extended signature. They are not
sound w.r.t. reduction for every CTRS, while they are complete w.r.t.
reduction. Here, soundness w.r.t. reduction means that every reduction sequence
of the corresponding unraveled TRS, of which the initial and end terms are over
the original signature, can be simulated by the reduction of the original CTRS.
In this paper, we show that an optimized variant of Ohlebusch's unraveling for
a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled
TRS is left-linear or both right-linear and non-erasing. We also show that
soundness of the variant implies that of Ohlebusch's unraveling. Finally, we
show that soundness of Ohlebusch's unraveling is the weakest in soundness of
the other unravelings and a transformation, proposed by Serbanuta and Rosu, for
(normal) deterministic CTRSs, i.e., soundness of them respectively implies that
of Ohlebusch's unraveling.Comment: 49 pages, 1 table, publication in Special Issue: Selected papers of
the "22nd International Conference on Rewriting Techniques and Applications
(RTA'11)
Complexity Bounds for Ordinal-Based Termination
`What more than its truth do we know if we have a proof of a theorem in a
given formal system?' We examine Kreisel's question in the particular context
of program termination proofs, with an eye to deriving complexity bounds on
program running times.
Our main tool for this are length function theorems, which provide complexity
bounds on the use of well quasi orders. We illustrate how to prove such
theorems in the simple yet until now untreated case of ordinals. We show how to
apply this new theorem to derive complexity bounds on programs when they are
proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability
Problems (RP 2014, 22-24 September 2014, Oxford
AC-KBO Revisited
Equational theories that contain axioms expressing associativity and
commutativity (AC) of certain operators are ubiquitous. Theorem proving methods
in such theories rely on well-founded orders that are compatible with the AC
axioms. In this paper we consider various definitions of AC-compatible
Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are
revisited. The former is enhanced to a more powerful version, and we modify the
latter to amend its lack of monotonicity on non-ground terms. We further
present new complexity results. An extension reflecting the recent proposal of
subterm coefficients in standard Knuth-Bendix orders is also given. The various
orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming
(TPLP) special issue for the 12th International Symposium on Functional and
Logic Programming (FLOPS 2014
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