Skip to content
This repository has been archived by the owner on Aug 30, 2023. It is now read-only.

Provides an implementation of a calculator that evaluates arithmetic expressions using Reverse Polish Notation (RPN).

Notifications You must be signed in to change notification settings

boostvolt/zhaw-pushdown-automata-upn

Repository files navigation

Push down automata UPN

To enable compound expressions to be written without parentheses, the Polish mathematician Jan Lukasiewicz designed a notation that lists the operators after the numbers and variables (and not in between). The notation is called Reverse Polish Notation1.

Instead of 3 + 4, one writes 3 4 +. This allows compound expressions to be written without parentheses and interpreted unambiguously. Another example: For (3+4)∗(6-2) one writes 3 4 + 6 2 - ∗. So first 3+4 is calculated, then 6 - 2 and finally the two factors are multiplied together. The result of the calculation is 28.

You can imagine that the numbers are written one after the other into the cellar or onto the stack. If an operator is read in (or comes as input), the two uppermost numbers are taken from the stack, calculated with each other and the result is put back on the stack.

PDA UPN validation

img.png

Note: Z is a number, O is an operator

flowchart LR
    START[ ] -- Start --> Q0((QO))
    Q0 -- Z,$/$ --> Q1(((Q1)))
    Q1 -- Z,$/Z$ --> Q2((Q2))
    Q2 -- Z,Z/ZZ<br/>O,Z/ε --> Q2
    Q2 -- ε,$/$ --> Q1

    style START fill:#FFFFFF00, stroke:#FFFFFF00;  
Loading

PDA UPN calculation

img_1.png

Note: Z is a number, O is an operator

flowchart LR
    START[ ] -- Start --> Q0(((Q0)))
    Q0 -- Z,$/#Z$ --> Q0
    Q0 -- Z,#/Z# --> Q1((Q1))
    Q1 -- Z,Z/ZZ --> Q1
    Q1 -- O,Z/ε --> Q2((Q2))
    Q2 -- ε,Z/Z --> Q1
    Q2 -- ε,#/ε --> Q3
    Q3((Q3)) -- ε,Z/#Z --> Q0

    style START fill:#FFFFFF00, stroke:#FFFFFF00;  
Loading

About

Provides an implementation of a calculator that evaluates arithmetic expressions using Reverse Polish Notation (RPN).

Topics

Resources

Stars

Watchers

Forks

Languages