ROBDD Constructor

An ROBDD constructor and SAT/unSAT solver written in C++, featured by LALR parsing

Implemented as class project, shared with love

Requirement

flex, bison for ROBDD frontend, graphviz for image generating.

flowchart LR
    subgraph Frontend
    Flex--"lexical symbol"-->Bison
    end
    subgraph Backend
    ROBDD
    end
    subgraph Visualization
    Graphviz
    end
    Bison<--"construct & reduce\nby LALR"-->ROBDD
    ROBDD--"format &\noutput"-->Graphviz

Loading

Usage

make ROBDD compile to binary first.

Usage: ROBDD [-SscAa] [-o filename]
 -S           - Check if the proposition is All-SAT
 -s           - Check if the proposition is Any-SAT
 -A           - Construct ROBDD under fixed ASCII order,
                smallest variable at top
 -a (default) - Construct ROBDD under parsing order
 -c           - Return SAT count for the proposition
 -t           - Return ROBDD construction time cost
 -o filename  - Print ROBDD to filename.svg

Note: -a is a heuristic approach, -A may result in over-sized ROBDD

Input your proposition then.

Syntax

Variable

For BDD, we take every variables as bool variables, which means they only take 0 or 1 as assignment. Each variable must start with letter (uppercase or lowercase), and can be a mixture of digits of letter, as regex [a-zA-Z]+[0-9]* suggests.

Operator

Symbol	Corresponding operation	Example	Priority
~	$\neg$ not	~a for $\neg a$	1
&	$\wedge$ and	a&b for $a\wedge b$	2
|	$\vee$ or	a|b for $a\wedge b$	2
=	$\leftrightarrow$ xnor	a=b for $a\leftrightarrow b$	2
!=	$\neq$ xor	a!=b for $a\neq b$	2
->	$\rightarrow$ infer	a->b for $a\rightarrow b$	3
()	pair of parentheses	(some formula here)	0

Smaller number means higher priority.

A valid proposition for example: Aa&B->C0|h

N Queens

There is a script n_queens_test/nqueens.py, you can use its output as ROBDD's input to test its correctness:

python n_queens_test/nqueens.py 6 | ./ROBDD -Ssc

Or print the output, an example is as below, for n > 6, visualization will take a long time.

6 queens

Todo

• Short Term

​ Move print module to visitor pattern, uncouple ROBDD from extensions

• Long Term

​ Use Bison C++ APIs, introduce std::shared_ptr for auto pruning

Credits

Henrik Reif Andersen, who wrote An Introduction to Binary Decision Diagrams and it's my major reference.