Skolem Machines

نویسندگان

  • John Fisher
  • Marc Bezem
چکیده

The Skolem machine is a Turing-complete machine model where the instructions are first-order formulas of a specific form. We introduce Skolem machines and prove their logical correctness and completeness. Skolem machines compute queries for the Geolog language, a rich fragment of first-order logic. The concepts of Geolog trees and complete Geolog trees are defined, and these tree concepts are used to show logical correctness and completeness of Skolem machine computations. The universality of Skolem machine computations is demonstrated. Lastly, the paper outlines implementation design issues using an abstract machine model approach.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Skolem Odd Difference Mean Graphs

In this paper we define a new labeling called skolem odd difference mean labeling and investigate skolem odd difference meanness of some standard graphs. Let G = (V,E) be a graph with p vertices and q edges. G is said be skolem odd difference mean if there exists a function f : V (G) → {0, 1, 2, 3, . . . , p + 3q − 3} satisfying f is 1−1 and the induced map f : E(G) → {1, 3, 5, . . . , 2q−1} de...

متن کامل

NP-completeness of generalized multi-Skolem sequences

A Skolem sequence is a sequence a1, a2, . . . , a2n (where ai ∈ A = {1, . . . , n}), each ai occurs exactly twice in the sequence and the two occurrences are exactly ai positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The existence question of deciding which sets of the form A = {1, . . . , n} are Skolem sets was solved by Thoralf Skolem [6] in 195...

متن کامل

Exponential lower bounds for the numbers of Skolem-type sequences

It was shown by Abrham that the number of pure Skolem sequences of order n, n ≡ 0 or 1 (mod 4), and the number of extended Skolem sequences of order n, are both bounded below by 2bn/3c. These results are extended to give similar lower bounds for the numbers of hooked Skolem sequences, split Skolem sequences and split-hooked Skolem sequences.

متن کامل

A note on the hardness of Skolem-type sequences

The purpose of this note is to give upper bounds (assuming P different from NP) on how far the generalizations of Skolem sequences can be taken while still hoping to resolve the existence question. We prove that the existence questions for both multi Skolem sequences and generalized Skolem sequences are strongly NP-complete. These results are significant strengthenings and simplifications of th...

متن کامل

Skolem labellings of generalised Dutch windmills

In this paper, we consider Skolem (vertex) labellings and present (hooked) Skolem labellings for generalised Dutch windmills whenever such labellings exist. Specifically, we show that generalised Dutch windmills with more than two cycles cannot be Skolem labelled and that those composed of two cycles of lengths m and n, n ≥ m, cannot be Skolem labelled if and only if n−m ≡ 3, 5 (mod 8) and m is...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Fundam. Inform.

دوره 91  شماره 

صفحات  -

تاریخ انتشار 2009