pyeda 0.22.0

Features

• Symbolic Boolean algebra with a selection of function representations:

  • Logic expressions

  • Truth tables, with three output states (0, 1, “don’t care”)

  • Reduced, ordered binary decision diagrams (ROBDDs)

• SAT solvers:

  • Backtracking

  • DPLL

  • PicoSAT

• Espresso logic minimization

• Formal equivalence

• Multi-dimensional bit vectors

• DIMACS CNF/SAT parsers

• Logic expression parser

Download

Bleeding edge code:

$ git clone git://github.com/cjdrake/pyeda.git

For release tarballs and zipfiles, visit PyEDA’s page at the Cheese Shop.

Installation

Latest released version using setuptools:

$ easy_install pyeda

Latest release version using pip:

$ pip install pyeda

Installation from the repository:

$ python setup.py install

Logic Expressions

Invoke your favorite Python terminal, and invoke an interactive pyeda session:

>>> from pyeda.inter import *

Create some Boolean expression variables:

>>> a, b, c, d = map(exprvar, "abcd")

Construct Boolean functions using overloaded Python operators: ~ (NOT), | (OR), ^ (XOR), & (AND), >> (IMPLIES):

>>> f0 = ~a & b | c & ~d
>>> f1 = a >> b
>>> f2 = ~a & b | a & ~b
>>> f3 = ~a & ~b | a & b
>>> f4 = ~a & ~b & ~c | a & b & c
>>> f5 = a & b | ~a & c

Construct Boolean functions using standard function syntax:

>>> f10 = Or(And(Not(a), b), And(c, Not(d)))
>>> f11 = Implies(a, b)
>>> f12 = Xor(a, b)
>>> f13 = Xnor(a, b)
>>> f14 = Equal(a, b, c)
>>> f15 = ITE(a, b, c)

Construct Boolean functions using higher order operators:

>>> f20 = Nor(a, b, c)
>>> f21 = Nand(a, b, c)
>>> f22 = OneHot(a, b, c)
>>> f23 = OneHot0(a, b, c)

Investigate a function’s properties:

>>> f0.support
frozenset({a, b, c, d})
>>> f0.inputs
(a, b, c, d)
>>> f0.top
a
>>> f0.degree
4
>>> f0.cardinality
16
>>> f0.depth
2

Factor complex expressions into only OR/AND and literals:

>>> f11.factor()
Or(~a, b)
>>> f12.factor()
Or(And(~a, b), And(a, ~b))
>>> f13.factor()
Or(And(~a, ~b), And(a, b))
>>> f14.factor()
Or(And(~a, ~b, ~c), And(a, b, c))
>>> f15.factor()
Or(And(a, b), And(~a, c))

Restrict a function’s input variables to fixed values, and perform function composition:

>>> f0.restrict({a: 0, c: 1})
Or(b, ~d)
>>> f0.compose({a: c, b: ~d})
Or(And(~c, ~d), And(c, ~d))

Test function formal equivalence:

>>> f2.equivalent(f12)
True
>>> f4.equivalent(f14)
True

Investigate Boolean identities:

# Law of double complement
>>> ~~a
a

# Idempotent laws
>>> a | a
a
>>> a & a
a

# Identity laws
>>> a | 0
a
>>> a & 1
a

# Dominance laws
>>> a | 1
1
>>> a & 0
0

# Commutative laws
>>> (a | b).equivalent(b | a)
True
>>> (a & b).equivalent(b & a)
True

# Associative laws
>>> a | (b | c)
Or(a, b, c)
>>> a & (b & c)
And(a, b, c)

# Distributive laws
>>> (a | (b & c)).to_cnf()
And(Or(a, b), Or(a, c))
>>> (a & (b | c)).to_dnf()
Or(And(a, b), And(a, c))

# De Morgan's laws
>>> Not(a | b).factor()
And(~a, ~b)
>>> Not(a & b).factor()
Or(~a, ~b)

# Absorption laws
>>> (a | (a & b)).absorb()
a
>>> (a & (a | b)).absorb()
a

Perform Shannon expansions:

>>> a.expand(b)
Or(And(a, ~b), And(a, b))
>>> (a & b).expand([c, d])
Or(And(a, b, ~c, ~d), And(a, b, ~c, d), And(a, b, c, ~d), And(a, b, c, d))

Convert a nested expression to disjunctive normal form:

>>> f = a & (b | (c & d))
>>> f.depth
3
>>> g = f.to_dnf()
>>> g
Or(And(a, b), And(a, c, d))
>>> g.depth
2
>>> f.equivalent(g)
True

Convert between disjunctive and conjunctive normal forms:

>>> f = ~a & ~b & c | ~a & b & ~c | a & ~b & ~c | a & b & c
>>> g = f.to_cnf()
>>> h = g.to_dnf()
>>> g
And(Or(a, b, c), Or(a, ~b, ~c), Or(~a, b, ~c), Or(~a, ~b, c))
>>> h
Or(And(~a, ~b, c), And(~a, b, ~c), And(a, ~b, ~c), And(a, b, c))

Multi-Dimensional Bit Vectors

Create some four-bit vectors, and use slice operators:

>>> A = exprvars('A', 4)
>>> B = exprvars('B', 4)
>>> A
[A[0], A[1], A[2], A[3]]
>>> A[2:]
[A[2], A[3]]
>>> A[-3:-1]
[A[1], A[2]]

Perform bitwise operations using Python overloaded operators: ~ (NOT), | (OR), & (AND), ^ (XOR):

>>> ~A
[~A[0], ~A[1], ~A[2], ~A[3]]
>>> A | B
[Or(A[0], B[0]), Or(A[1], B[1]), Or(A[2], B[2]), Or(A[3], B[3])]
>>> A & B
[And(A[0], B[0]), And(A[1], B[1]), And(A[2], B[2]), And(A[3], B[3])]
>>> A ^ B
[Xor(A[0], B[0]), Xor(A[1], B[1]), Xor(A[2], B[2]), Xor(A[3], B[3])]

Reduce bit vectors using unary OR, AND, XOR:

>>> A.uor()
Or(A[0], A[1], A[2], A[3])
>>> A.uxor()
Xor(A[0], A[1], A[2], A[3])
>>> A.uand()
And(A[0], A[1], A[2], A[3])

Create and test functions that implement non-trivial logic such as arithmetic:

>>> from pyeda.logic.addition import *
>>> S, C = ripple_carry_add(A, B)
# Note "1110" is LSB first. This says: "7 + 1 = 8".
>>> S.vrestrict({A: "1110", B: "1000"}).to_uint()
8

Other Function Representations

Consult the documentation for information about truth tables, and binary decision diagrams. Each function representation has different trade-offs, so always use the right one for the job.

PicoSAT SAT Solver C Extension

PyEDA includes an extension to the industrial-strength PicoSAT SAT solving engine.

Use the satisfy_one method to finding a single satisfying input point:

>>> f = OneHot(a, b, c)
>>> f.satisfy_one()
{a: 0, b: 0, c: 1}

Use the satisfy_all method to iterate through all satisfying input points:

>>> list(f.satisfy_all())
[{a: 0, b: 0, c: 1}, {a: 0, b: 1, c: 0}, {a: 1, b: 0, c: 0}]

For more interesting examples, see the following documentation chapters:

• Solving Sudoku

• All Solutions to the Eight Queens Puzzle

Espresso Logic Minimization C Extension

PyEDA includes an extension to the famous Espresso library for the minimization of two-level covers of Boolean functions.

Use the espresso_exprs function to minimize multiple expressions:

>>> f1 = ~a & ~b & ~c | ~a & ~b & c | a & ~b & c | a & b & c | a & b & ~c
>>> f2 = ~a & ~b & c | a & ~b & c
>>> f1m, f2m = espresso_exprs(f1, f2)
>>> f1m
Or(And(~a, ~b), And(a, b), And(~b, c))
>>> f2m
And(~b, c)

Use the espresso_tts function to minimize multiple truth tables:

>>> X = exprvars('x', 4)
>>> f1 = truthtable(X, "0000011111------")
>>> f2 = truthtable(X, "0001111100------")
>>> f1m, f2m = espresso_tts(f1, f2)
>>> f1m
Or(x[3], And(x[0], x[2]), And(x[1], x[2]))
>>> f2m
Or(x[2], And(x[0], x[1]))

Execute Unit Test Suite

If you have Nose installed, run the unit test suite with the following command:

$ make test

If you have Coverage installed, generate a coverage report (including HTML) with the following command:

$ make cover

Perform Static Lint Checks

If you have Pylint installed, perform static lint checks with the following command:

$ make lint

Build the Documentation

If you have Sphinx installed, build the HTML documentation with the following command:

$ make html

Python Versions Supported

PyEDA is developed using Python 3.2+. It is NOT compatible with Python 2.7.

Contact the Authors

• Chris Drake (cjdrake AT gmail DOT com), http://cjdrake.blogspot.com