Complexity Analysis of Tree Share Operations

نویسندگان

  • Xuan-Bach Le
  • Aquinas Hobor
  • Anthony W. Lin
چکیده

We investigate the complexity of the tree share model of Dockins et al., which is used to reason about shared ownership of resources in e.g. concurrent programs. We obtain the precise complexity for first-order theory of the full Boolean algebra of tree shares (that is, with all tree-share constants) which is the same as first-order theory of countably atomless Boolean algebras (that is, where the only constants allowed in formulas are 0 and 1); the previous bound was nonelementary (that is, not bounded by any fixed tower of exponentials). We also prove a precise complexity bound on the first-order theory over the “relativization” multiplication operator on trees if one operand is a constant; the previous bound was non-elementary if the constant was on the right and not known to be decidable if the constant was on the left. Finally, we prove that the first-order theory over the structure that combines the Boolean algebra operators and the right-handed multiplication has a non-elementary lower bound even though the key subtheories are elementary, showing that the existing non-elementary upper bound cannot be improved. 1998 ACM Subject Classification F.1.1 Models of Computation, F.3.1 Specifying and Verifying and Reasoning about Programs, F.4.1 Mathematical Logic, F.4.3 Formal Languages

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

Decidability and Complexity of Tree Share Formulas

Fractional share models are used to reason about how multiple actors share ownership of resources. We examine the decidability and complexity of reasoning over the “tree share” model of Dockins et al. using first-order logic, or fragments thereof. We pinpoint a connection between the basic operations on trees union t, intersection u, and complement and countable atomless Boolean algebras, allow...

متن کامل

An improved algorithm to reconstruct a binary tree from its inorder and postorder traversals

It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of...

متن کامل

A method for analyzing the problem of determining the maximum common fragments of temporal directed tree, that do not change with time

In this study two actual types of problems are considered and solved: 1) determining the maximum common connected fragment of the T-tree (T-directed tree) which does not change with time; 2) determining all maximum common connected fragments of the T-tree (T-directed tree) which do not change with time. The choice of the primary study of temporal directed trees and trees is justified by the wid...

متن کامل

Complexity Analysis of Tree Share Structure

We investigate the complexity of the tree share model of Dockins et al., which is used to reason about shared ownership of resources in concurrent programs. We obtain the precise Berman complexity for the first-order theory of the Boolean algebra of tree shares with constants, which is STA(∗, 2 O(1) , n)-complete. For the first-order theory over the “relativization” multiplication operator on t...

متن کامل

An improved algorithm to reconstruct a binary tree from its inorder and postorder traversals

It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017