Topic
Operator associativity
About: Operator associativity is a research topic. Over the lifetime, 26 publications have been published within this topic receiving 217 citations. The topic is also known as: associativity.
Papers
5 May 1969
TL;DR: The operator precedence languages are shown to be a proper subset of the backwards-deterministic Wirth-Weber precedence languages which in turn are a proper subclass of the deterministic context-free languages.
Abstract: The classes of languages definable by operator precedence grammars1 and by Wirth-Weber precedence grammars2 are studied. A grammar is backwards-deterministic3 if no two productions have the same right part. Operator precedence grammars have no more generative power than backwards deterministic operator precedence grammars, but Wirth-Weber precedence grammars (i.e., grammars having unique Wirth-Weber precedence relations) are more powerful than backwards-deterministic Wirth-Weber precedence grammars; indeed they can generate any context-free language. An algorithm is developed for finding a Wirth-Weber precedence grammar equivalent to a given operator precedence grammar, a result of possible practical significance. The operator precedence languages are shown to be a proper subclass of the backwards-deterministic Wirth-Weber precedence languages which in turn are a proper subclass of the deterministic context-free languages.
61 citations
Patent•
3 Nov 2000
TL;DR: In this article, a mathematical operation consisting of the operand, the operation symbol and the operator is illustrated, and a solution to the operator's operation is illustrated; the operator objects also include a non-numerical representation of the value of the operator.
Abstract: A system uses objects that can be combined to learn mathematical operations. Operand objects illustrate a numerical operand and an associated set of possible numerical solutions to operations performed on the operand number. Operator objects illustrate an operation symbol and a numerical operator. When an operator object and an operand object are combined, a mathematical operation consisting of the operand, the operation symbol and the operator is illustrated, and a solution to the operation is illustrated. The operand objects also include a non-numerical representation of the value of the operand, and the operator objects also include a non-numerical representation of the value of the operator. When combined, the representation of the value of the operator, and the representation of the value of the operand cooperate to represent the value of the solution to the mathematical operation.
25 citations
TL;DR: A generalization of the t-conorm aggregation operator is defined, which relaxes the requirement of associativity, and these operators are named as GENOR operators, which allow us to control the reinforcement process.
Abstract: We describe the basic features of the t-norm operator and then introduce a family of t-norm operators that are defined on an ordinal space. We then do the same for the t-conorms. We note the strong limitation that the requirement of associativity places on the t-norm and t-conorm operators. We particularly note how it limits our ability to model different types of reinforcement. We then define a generalization of the t-conorm aggregation operator, which relaxes the requirement of associativity, we denote these operators as GENOR operators. We show that these operators have the same functionality as the t-conorm. We provide some examples of GENOR operators which allow us to control the reinforcement process. We define a related extension for the t-norm, the GENAND operator and provide some examples.
15 citations
TL;DR: Among the theoretical results obtained are a characterization of the structure of precedence relations and the relation of canonical precedence schemes to operator sets.
Abstract: A general theory of canonical precedence analysis is defined and studied. The familiar types of precedence analysis such as operator precedence or simple precedence occur as special cases of this theory. Among the theoretical results obtained are a characterization of the structure of precedence relations and the relation of canonical precedence schemes to operator sets.
15 citations
TL;DR: It is shown that any arithmetic expression with n operands and parentheses nested to depth d can be evaluated in at most 1+2d+ [log2n] steps, assuming that only associativity and commutativity are used to transform the expression.
Abstract: We show that any arithmetic expression with n operands and parentheses nested to depth d can be evaluated in at most 1+2d+ [log2 n] steps, assuming that only associativity and commutativity are used to transform the expression. We also show that at most [n?2d/2] processors are needed to achieve this bound.
14 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 2 |
| 2016 | 1 |
| 2015 | 2 |
| 2009 | 1 |
| 2008 | 1 |
| 2007 | 1 |