Doing Arithmetic with Diagrams
نویسنده
چکیده
A theorem prover f o r part of ar i thmet ic in described which proves theorems by represent ing them in the form of a diagram or network. The nodes of t h i s network represent ' i d e a l i n t e g e r s ' , i . e . objects which have a l l the propert ies of in tegers , without being any p a r t i cular in toger . The l i nks in the network represent re la t ionsh ips between ' i dea l i n t e g e r s ' . The procedures which draw these diagrams make elementary deductions based on t h e i r b u i l t i n knowledge of the funct ions and predicates of a r i thmet i c . This theorem prover is intended as a model of some kinds of human problemso lv ing behaviour.
منابع مشابه
Transient Analysis of Stochastic Petri Nets With Interval Decision Diagrams
This paper presents an Interval Decision Diagram (IDD) based approach to realize symbolically transient analysis of Continuous Time Markov Chains (CTMC) which are derived from stochastic Petri nets. Matrix-vector and vector-matrix multiplication are the major tasks when doing exact analysis of CTMCs. We sketch a simple algorithm which uses explicitly the Petri net structure and offers the oppor...
متن کاملA Unifying Approach to Edge-valued and Arithmetic Transform Decision Diagrams
This paper shows that binary decision diagrams (BDDs) and their generalizations are not only representations of switching and integer-valued functions, but also Fourier-like series expansions of them. Furthermore, it shows that edge-valued binary decision diagrams (EVBDDs) are related to arithmetic transform decision diagrams (ACDDs), which are the integer counterparts of the functional decisio...
متن کاملPOSSIBLE m-DIAGRAMS OF MODELS OF ARITHMETIC
In this paper we investigate the complexity of m-diagrams of models of various completions of first-order Peano Arithmetic (PA). We obtain characterizations that extend Solovay’s results for open diagrams of models of completions of PA. We first characterize the m-diagrams of models of True Arithmetic by showing that the degrees ofm-diagrams of nonstandard models A of TA are the same for allm ≥...
متن کاملRestructuring of Arithmetic Circuits with Biconditional Binary Decision Diagrams
Biconditional Binary Decision Diagrams (BBDDs) are a novel class of canonical binary decision diagrams where the branching condition, and its associated logic expansion, is biconditional on two variables. In this demonstration, we use an efficient BBDD manipulation package as front-end to a commercial synthesis tool to restructure arithmetic operations in critical components of telecommunicatio...
متن کاملEvaluating influence diagrams with decision circuits
Although a number of related algorithms have been developed to evaluate influence diagrams, exploiting the conditional independence in the diagram, the exact solution has remained intractable for many important problems. In this paper we introduce decision circuits as a means to exploit the local structure usually found in decision problems and to improve the performance of influence diagram an...
متن کامل