The original README follows.
Hello all,
I have moved on from this project, and will not spend time on maintenance or bug fixes. I welcome any discussion in Issues. I also welcome forks of any kind, for any reason.
PyEDA is a Python library for electronic design automation.
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
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 release version using pip:
$ pip3 install pyeda
Latest release version using conda and conda-forge:
$ conda install pyeda
Installation from the repository:
$ python3 setup.py install
Note that you will need to have Python headers and libraries in order to compile the C extensions. For MacOS, the standard Python installation should have everything you need. For Linux, you will probably need to install the Python3 “development” package.
For Debian-based systems (eg Ubuntu, Mint):
$ sudo apt-get install python3-dev
For RedHat-based systems (eg RHEL, Centos):
$ sudo yum install python3-devel
For Windows, just grab the binaries from Christoph Gohlke’s excellent pythonlibs page.
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) >>> f16 = Nor(a, b, c) >>> f17 = Nand(a, b, c)
Construct Boolean functions using higher order operators:
>>> OneHot(a, b, c) And(Or(~a, ~b), Or(~a, ~c), Or(~b, ~c), Or(a, b, c)) >>> OneHot0(a, b, c) And(Or(~a, ~b), Or(~a, ~c), Or(~b, ~c)) >>> Majority(a, b, c) Or(And(a, b), And(a, c), And(b, c)) >>> AchillesHeel(a, b, c, d) And(Or(a, b), Or(c, d))
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
Convert expressions to negation normal form (NNF), with only OR/AND and literals:
>>> f11.to_nnf() Or(~a, b) >>> f12.to_nnf() Or(And(~a, b), And(a, ~b)) >>> f13.to_nnf() Or(And(~a, ~b), And(a, b)) >>> f14.to_nnf() Or(And(~a, ~b, ~c), And(a, b, c)) >>> f15.to_nnf() Or(And(a, b), And(~a, c)) >>> f16.to_nnf() And(~a, ~b, ~c) >>> f17.to_nnf() Or(~a, ~b, ~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:
# Double complement >>> ~~a a # Idempotence >>> a | a a >>> And(a, a) a # Identity >>> Or(a, 0) a >>> And(a, 1) a # Dominance >>> Or(a, 1) 1 >>> And(a, 0) 0 # Commutativity >>> (a | b).equivalent(b | a) True >>> (a & b).equivalent(b & a) True # Associativity >>> Or(a, Or(b, c)) Or(a, b, c) >>> And(a, And(b, c)) And(a, b, c) # Distributive >>> (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 >>> Not(a | b).to_nnf() And(~a, ~b) >>> Not(a & b).to_nnf() Or(~a, ~b)
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
farray([a[0], a[1], a[2], a[3]])
>>> A[2:]
farray([a[2], a[3]])
>>> A[-3:-1]
farray([a[1], a[2]])
Perform bitwise operations using Python overloaded operators: ~ (NOT), | (OR), & (AND), ^ (XOR):
>>> ~A farray([~a[0], ~a[1], ~a[2], ~a[3]]) >>> A | B farray([Or(a[0], b[0]), Or(a[1], b[1]), Or(a[2], b[2]), Or(a[3], b[3])]) >>> A & B farray([And(a[0], b[0]), And(a[1], b[1]), And(a[2], b[2]), And(a[3], b[3])]) >>> A ^ B farray([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.uand() And(a[0], a[1], a[2], a[3]) >>> A.uxor() Xor(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:
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 = Or(~a & ~b & ~c, ~a & ~b & c, a & ~b & c, a & b & c, a & b & ~c) >>> f2 = Or(~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 PyTest 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 3.3+. It is NOT compatible with Python 2.7, or Python 3.2.
Citations
I recently discovered that people actually use this software in the real world. Feel free to send me a pull request if you would like your project listed here as well.
A Model-Based Approach for Reliability Assessment in Component-Based Systems
bunsat, used for the SAT paper Fast DQBF Refutation
Input-Aware Implication Selection Scheme Utilizing ATPG for Efficient Concurrent Error Detection
Generation Methodology for Good-Enough Approximate Modules of ATMR
Effect of FPGA Circuit Implementation on Error Detection Using Logic Implication Checking
Presentations
Video from SciPy 2015
1 maintainer
Metadata
1 maintainer
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