py-aiger-discrete 0.1.2

Library for modeling functions over discrete sets using aiger circuits.

py-aiger-discrete

Library for modeling functions over discrete sets using aiger circuits.

Installation

If you just need to use py-aiger-discrete, you can just run:

$ pip install py-aiger-discrete

For developers, note that this project uses the poetry python package/dependency management tool. Please familarize yourself with it and then run:

$ poetry install

About

This library helps with modeling functions over finite sets using circuits.

f : A → B₁ × B₂ × … × Bₘ

where A ⊆ A₁ × A₂ × … × Aₙ.

This is done by providing:

1. A encoder/decoder pair for each set to and from (unsigned) integers.
2. A circuit that uses the bit-vector representation of these integers to compute f.
3. A circuit that monitors if the input bit-vector sequence is valid, i.e., a member of A.

Functionally, the py-aiger-discrete library centers around the aiger_discrete.FiniteFunc class which has 4 attributes an aiger_bv.AIGBV object.

1. A string valid_id indicating
2. A circuit, circ, over named bit-vectors in the form of an aiger_bv.AIGBV object. One of the outputs must be named valid_id.
3. A mapping from inputs to aiger_discrete.Encoding objects which encode/decode objects to integers. The standard bit-encoding of unsigned integers is feed into circ.
4. A mapping from outputs to aiger_discrete.Encoding objects which encode/decode objects to integers. These encodings are used to decode the resulting bit-vectors of circ.

Usage

Below we provide a basic usage example. This example assumes basic knowledge of the py-aiger ecosystem and particularly py-aiger-bv.

import aiger_bv as BV

from aiger_discrete import Encoding, from_aigbv

# Will assume inputs are in 'A', 'B', 'C', 'D', or 'E'.
ascii_encoder = Encoding(
    decode=lambda x: chr(x + ord('A')),  # Make 'A' map to 0.
    encode=lambda x: ord(x) - ord('A'),
)

# Create function which maps: A -> B, B -> C, C -> D, D -> E.

x = BV.uatom(3, 'x')  # need 3 bits to capture 5 input types.
update_expr = (x + 1) & 0b111
circ = update_expr.with_output('y').aigbv

# Need to assert that the inputs are less than 4.
circ |= (x <= 4).with_output('##valid').aigbv

func = from_aigbv(
    circ,
    input_encodings={'x': ascii_encoder},
    output_encodings={'y': ascii_encoder},
    valid_id='##valid',
)

assert func('A') == 'B'
assert func('B') == 'C'
assert func('C') == 'D'
assert func('D') == 'E'
assert func('E') == 'A'

Note that py-aiger-discrete implements most of the circuit API as aiger_bv.AIGBV.

For example, sequential composition:

func12 = func1 >> func2

or parallel composition:

func12 = func1 | func2

or unrolling:

func_unrolled = func1.unroll(5)

or feedback:

func_cycle = func1.loopback({
    'input': 'x',
    'output': 'y',
    'keep_output': True,
    `input_encoder`: True,
    `init`: 'A',
})

Note that feedback now supports additional flag per wiring description called input_encoder which determines if the input or output encoding is used for initial latch value resp. The default is the input encoding.

or renaming:

func_renamed = func1['i', {'x': 'z'}]
assert func1.inputs == {'z'}