177 research outputs found
Order-Sorted Unification with Regular Expression Sorts
We extend first-order order-sorted unification by permitting regular expression sorts for variables and in the domains of function symbols. The set of basic sorts is finite. The obtained signature corresponds to a finite bottom-up hedge automaton. The unification problem in such a theory generalizes some known unification problems. Its unification type is infinitary. We give a complete unification procedure and prove decidability
Enumerating All Maximal Clique-Partitions of an Undirected Graph
We address the problem of enumerating all maximal clique-partitions of an
undirected graph and present an algorithm based on the observation that every
maximal clique-partition can be produced from the maximal clique-cover of the
graph by assigning the vertices shared among maximal cliques, to belong to only
one clique. This simple algorithm has the following drawbacks: (1) the search
space is very large; (2) it finds some clique-partitions which are not maximal;
and (3) some clique-partitions are found more than once. We propose two
criteria to avoid these drawbacks. The outcome is an algorithm that explores a
much smaller search space and guarantees that every maximal clique-partition is
computed only once. The algorithm can be used in problems such as
anti-unification with proximity relations or in resource allocation tasks when
one looks for several alternative ways to allocate resources.Comment: In Proceedings FROM 2023, arXiv:2309.1295
Constraint Solving over Multiple Similarity Relations
Similarity relations are reflexive, symmetric, and transitive fuzzy relations. They help to make approximate inferences, replacing the notion of equality. Similarity-based unification has been quite intensively investigated, as a core computational method for approximate reasoning and declarative programming. In this paper we consider solving constraints over several similarity relations, instead of a single one. Multiple similarities pose challenges to constraint solving, since we can not rely on the transitivity property anymore. Existing methods for unification with fuzzy proximity relations (reflexive, symmetric, non-transitive relations) do not provide a solution that would adequately reflect particularities of dealing with multiple similarities. To address this problem, we develop a constraint solving algorithm for multiple similarity relations, prove its termination, soundness, and completeness properties, and discuss applications
Regular matching problems for infinite trees
We investigate regular matching problems. The classical reference is Conway's
textbook "Regular algebra and finite machines". Some of his results can be
stated as follows. Let and be
regular languages where is a set of constants and is a set of
variables. Substituting every by a regular subset of
yields a regular set . A substitution
solves a matching problem "?" if .
There are finitely many maximal solutions ; they are effectively
computable and is regular for all ; and every solution is
included in a maximal one. Also, in the case of words
"?" is decidable.
Apart from the last property, we generalize these results to infinite trees.
We define a notion of choice function which for any tree over
and position of a variable selects at most one tree
; next, we define as the limit of a
Cauchy sequence; and the union over all yields .
Since our definition coincides with that for IO substitutions, we write
instead of .
Our main result is the decidability of
"?" if is regular and belongs
to a class of tree languages closed under intersection with regular sets. Such
a special case pops up if is context-free. Note that
"?" is undecidable, in general in that case.
However, the decidability of "?" if both
and are regular remains open because, in contrast to word languages, the
homomorphic image of a regular tree language is not always regular if
is regular for all .Comment: 18 pages. This replacement eliminates a false claim from the previous
arXiv version of this paper: Item 4 of Theorem 1 did not hold for # = {=
Generic Encodings of Constructor Rewriting Systems
Rewriting is a formalism widely used in computer science and mathematical
logic. The classical formalism has been extended, in the context of functional
languages, with an order over the rules and, in the context of rewrite based
languages, with the negation over patterns. We propose in this paper a concise
and clear algorithm computing the difference over patterns which can be used to
define generic encodings of constructor term rewriting systems with negation
and order into classical term rewriting systems. As a direct consequence,
established methods used for term rewriting systems can be applied to analyze
properties of the extended systems. The approach can also be seen as a generic
compiler which targets any language providing basic pattern matching
primitives. The formalism provides also a new method for deciding if a set of
patterns subsumes a given pattern and thus, for checking the presence of
useless patterns or the completeness of a set of patterns.Comment: Added appendix with proofs and extended example
Research on corn hybrids behavior under the application of new technological concepts in Osmancea-Constanta area
The emergence of new growing concepts aiming to achieve the biological yield potential of crops, soil conservation and the increase in economic efficiency, had also an echo in the agriculture of Dobrogea area. Farmers were involved in finding the best solutions to achieve these goals. Research conducted at SC Micul Agricultor SRL farm, located in Osmancea, Constanta County is an example in this direction. This research aimed to establish the corn hybrids best adapted to the climatic and pedologic conditions of the area, and the most efficient soil tillage system and to optimize crop fertilization. For this purpose, the behavior of Mas 40 F, Dartona and P 9911 corn hybrids was studied under conventional (plowing) and minimum soil tillage (tiger and disk) for the following fertilization levels: unfertilized, N90P40K40 and N90P40K40 + Greenstart - 25 kg/ha.The best results were obtained when using tiger to perform basic soil tillage and fertilizing with N90P40K40 + 25 kg/ha Greenstart. For this variant, all hybrids had the highest yields ranging from 13.56 to 13.93 t/h
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