The trivialib.bdd Reference Manual

Table of Contents

The trivialib.bdd Reference Manual

This is the trivialib.bdd Reference Manual, version 0.1, generated automatically by Declt version 3.0 "Montgomery Scott" on Fri Jun 26 12:31:42 2020 GMT+0.

1 Introduction

* Trivialib.Bdd 

Functional implementation of (Ordered) Binary Decision Diagram (BDD) and Zero-suppressed Binary Decision Diagram (ZDD).

+ Bryant, Randal E. "Graph-based algorithms for boolean function
  manipulation." Computers, IEEE Transactions on 100.8 (1986): 677-691.
+ Minato, Shin-ichi. "Zero-suppressed BDDs for set manipulation in
  combinatorial problems." Design Automation, 1993. 30th Conference
  on. IEEE, 1993.

[[http://users.cecs.anu.edu.au/~ssanner/AAAI16/][Tutorial slide]] on Symbolic Methods for Hybrid Inference, Optimization, and Decision-making at AAAI 2016, by [[http://users.cecs.anu.edu.au/~ssanner/][Scott Sanner]]

* FEATURES

Based on structures --- moderately fast

Weak hash table --- GC-aware, moderate memory usage

Pattern matching --- functional, clean implementation

* TODOs

+ more useful interfaces for set manipulation, function manipulation
+ speed
+ extension to ADD (Algebraic Decision Diagram) --- mostly trivial
+ extension to XADD (algebraic decision diagram)
+ extension to MV-DDs (multi-valued decision diagram)
+ extension to AADDs (affine algebrainc decision diagram) --- for representing formula
+ extension to XADDs (continuous variable extension of algebrainc decision diagram) --- for continuous range
+ extension to SDD (sentensial decision diagram)

* Usage

Web API Documentation will be available at http://quickdocs.org/trivialib.bdd/

#+BEGIN_SRC lisp

;; Knuth Chapter 4, figure 12 (and 122), rightmost ("kernel")
;; represent a set {{1,3,5},{1,4},{2,4,6},{2,5},{3,6}}
(labels ((add2 (dd1 dd2) (odd-apply dd1 dd2 (lambda (a b) (or a b))))
         (mul2 (dd1 dd2) (odd-apply dd1 dd2 (lambda (a b) (and a b))))
         (add (dd1 dd2 &rest args)
           (if args
               (apply #'add (add2 dd1 dd2) args)
               (add2 dd1 dd2)))
         (mul (dd1 dd2 &rest args)
           (if args
               (apply #'mul (mul2 dd1 dd2) args)
               (mul2 dd1 dd2)))
         (o (x) (odd (unit x)))
         (x (x) (odd (!unit x)))
         (change-many (node &rest args) (reduce #'change args :initial-value node)))

  (with-odd-context (:variable '(a b c d e f))
    ;; stored into VARIABLES slot of an ODD. ^^^
    ;; Different variable orderings make ODDs incompatible.
    (gcprint
     ;; using BDD reduction rule: 15 nodes
     (add (mul (o 1) (x 2) (o 3) (x 4) (o 5) (x 6))
          (mul (o 1) (x 2) (x 3) (o 4) (x 5) (x 6))
          (mul (x 1) (o 2) (x 3) (o 4) (x 5) (o 6))
          (mul (x 1) (o 2) (x 3) (x 4) (o 5) (x 6))
          (mul (x 1) (x 2) (o 3) (x 4) (x 5) (o 6)))))
  (with-odd-context (:operation #'zdd-apply)
    ;; Different reduction rule also make ODDs incompatible.
    (gcprint
     ;; using Zero-suppressed reduction rule: 8 nodes
     (add (odd (change-many (leaf t) 1 3 5))
          (odd (change-many (leaf t) 1 4))
          (odd (change-many (leaf t) 2 4 6))
          (odd (change-many (leaf t) 2 5))
          (odd (change-many (leaf t) 3 6)))))
  (with-odd-context (:operation #'zdd-apply)
    ;; using a utility function for ZDD
    (gcprint
     (add (odd (make-set '(1 3 5)))
          (odd (make-set '(1 4)))
          (odd (make-set '(2 4 6)))
          (odd (make-set '(2 5)))
          (odd (make-set '(3 6))))))
  (with-odd-context (:operation #'zdd-apply)
    ;; using a utility function for ZDD
    (gcprint
     (odd (make-family '((1 3 5)
                         (1 4)
                         (2 4 6)
                         (2 5)
                         (3 6)))))))
#+END_SRC

** Dependencies

This library is at least tested on implementation listed below:

+ SBCL 1.2.8 on X86-64 Linux  3.13.0-46-generic (author's environment)

Also, it depends on the following libraries:

+ alexandria by  ::
    Alexandria is a collection of portable public domain utilities.

+ trivia by Masataro Asai ::
    NON-optimized pattern matcher compatible with OPTIMA, with extensible optimizer interface and clean codebase

+ immutabe-struct by Masataro Asai :: 

+ trivial-garbage :: For handling weak hash tables.
    
** Author

+ Masataro Asai (guicho2.71828@gmail.com)

* Copyright

Copyright (c) 2015 Masataro Asai (guicho2.71828@gmail.com)


* License

Licensed under the LLGPL License.

2 Systems

The main system appears first, followed by any subsystem dependency.

2.1 trivialib.bdd

Author

Masataro Asai

Contact

guicho2.71828@gmail.com

License

LLGPL

Description

BDD and ZDD implementation using Trivia

Version

0.1

Dependencies

• alexandria
• trivia
• trivial-garbage
• immutable-struct

Source

trivialib.bdd.asd (file)

Components

• 0.package.lisp (file)
• 1.struct.lisp (file)
• 2.odd.lisp (file)
• 3.bdd.lisp (file)
• 4.zdd.lisp (file)

3 Files

Files are sorted by type and then listed depth-first from the systems components trees.

3.1 Lisp

3.1.1 trivialib.bdd.asd

Location

/home/quickref/quicklisp/dists/quicklisp/software/trivialib.bdd-20180328-git/trivialib.bdd.asd

Systems

trivialib.bdd (system)

3.1.2 trivialib.bdd/0.package.lisp

Parent

trivialib.bdd (system)

Location

0.package.lisp

Packages

trivialib.bdd

3.1.3 trivialib.bdd/1.struct.lisp

Dependency

0.package.lisp (file)

Parent

trivialib.bdd (system)

Location

1.struct.lisp

Exported Definitions

• leaf (function)
• leaf (structure)
• node (structure)

Internal Definitions

• *leaf-cache* (special variable)
• *node-cache* (special variable)
• *variables* (special variable)
• copy-leaf (function)
• copy-node (function)
• leaf-content (function)
• (setf leaf-content) (function)
• leaf-p (function)
• make-leaf (function)
• make-node (function)
• node-hi (function)
• (setf node-hi) (function)
• node-lo (function)
• (setf node-lo) (function)
• node-p (function)
• node-variable (function)
• (setf node-variable) (function)

3.1.4 trivialib.bdd/2.odd.lisp

Dependency

1.struct.lisp (file)

Parent

trivialib.bdd (system)

Location

2.odd.lisp

Exported Definitions

• call-with-odd-context (function)
• odd (function)
• odd (structure)
• odd-apply (function)
• with-odd-context (macro)

Internal Definitions

• *operation* (special variable)
• copy-odd (function)
• make-odd (function)
• odd-compatible-p (function)
• odd-node-cache (function)
• odd-operation (function)
• odd-p (function)
• odd-root (function)
• odd-variables (function)

3.1.5 trivialib.bdd/3.bdd.lisp

Dependency

2.odd.lisp (file)

Parent

trivialib.bdd (system)

Location

3.bdd.lisp

Exported Definitions

• !unit (function)
• bdd (function)
• bdd-apply (function)
• bdd-node (function)
• unit (function)

3.1.6 trivialib.bdd/4.zdd.lisp

Dependency

3.bdd.lisp (file)

Parent

trivialib.bdd (system)

Location

4.zdd.lisp

Exported Definitions

• change (function)
• make-family (function)
• make-set (function)
• zdd (function)
• zdd-apply (function)
• zdd-node (function)

4 Packages

Packages are listed by definition order.

4.1 trivialib.bdd

Source

0.package.lisp (file)

Use List

• trivia.level2
• alexandria
• common-lisp

Exported Definitions

• !unit (function)
• bdd (function)
• bdd-apply (function)
• bdd-node (function)
• call-with-odd-context (function)
• change (function)
• leaf (function)
• leaf (structure)
• make-family (function)
• make-set (function)
• node (structure)
• odd (function)
• odd (structure)
• odd-apply (function)
• unit (function)
• with-odd-context (macro)
• zdd (function)
• zdd-apply (function)
• zdd-node (function)

Internal Definitions

• *leaf-cache* (special variable)
• *node-cache* (special variable)
• *operation* (special variable)
• *variables* (special variable)
• copy-leaf (function)
• copy-node (function)
• copy-odd (function)
• leaf-content (function)
• (setf leaf-content) (function)
• leaf-p (function)
• make-leaf (function)
• make-node (function)
• make-odd (function)
• node-hi (function)
• (setf node-hi) (function)
• node-lo (function)
• (setf node-lo) (function)
• node-p (function)
• node-variable (function)
• (setf node-variable) (function)
• odd-compatible-p (function)
• odd-node-cache (function)
• odd-operation (function)
• odd-p (function)
• odd-root (function)
• odd-variables (function)

5 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.

5.1 Exported definitions

5.1.1 Macros

Macro: with-odd-context (&key DEFAULT VARIABLES NODE-CACHE OPERATION &allow-other-keys) &body BODY

Execute BODY in a dynamic environment where the context variables (‘*VARIABLES*’ , ‘*NODE-CACHE*’ and ‘*OPERATION*’) are set. DEFAULT should be nil or an ODD object, in which case
the context variables are inherited by the given ODD.

Package

trivialib.bdd

Source

2.odd.lisp (file)

5.1.2 Functions

Function: !unit VARIABLE

Returns a BDD node whose HI node is a terminal node of NIL and LO node is a terminal node of T (opposite to UNIT). Useful for representing a boolean variable.

Package

trivialib.bdd

Source

3.bdd.lisp (file)

Function: bdd ROOT &optional VARIABLES NODE-CACHE

Shortcut for instantiating an ODD using BDD-APPLY.

Package

trivialib.bdd

Source

3.bdd.lisp (file)

Function: bdd-apply F G OP-LEAF

APPLY rule for BDD.

Package

trivialib.bdd

Source

3.bdd.lisp (file)

Function: bdd-node VARIABLE HI LO

Node generation & pruning rule for BDD.

Package

trivialib.bdd

Source

3.bdd.lisp (file)

Function: call-with-odd-context DEFAULT VARIABLES NODE-CACHE OPERATION BODY-FN

Function version of WITH-ODD-CONTEXT.

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: change F VARIABLE

Change operation defined in MINATO et al. 93’. Flip the existense of a given variable in the family of sets. Examples:
(change {{1,3} {2,5}} 6) –> {{1,3,6} {2,5,6}}
(change {{1,3} {2,5,6}} 6) –> {{1,3,6} {2,5}}

Package

trivialib.bdd

Source

4.zdd.lisp (file)

Function: leaf THING

Return the leaf node in the hash table *leaf-cache*, creating an instance when required

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: make-family FAMILIES

Example: (make-family ’((1 3 5) (2 4))) –> a zdd representing {{1,3,5},{2,4}}

Package

trivialib.bdd

Source

4.zdd.lisp (file)

Function: make-set VARIABLES

Example: (make-set ’(1 3 5)) –> a zdd representing {{1,3,5}}

Package

trivialib.bdd

Source

4.zdd.lisp (file)

Function: odd &optional ROOT VARIABLES NODE-CACHE OPERATION

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: odd-apply ODD1 ODD2 LEAF-OPERATION

Applies the operation stored in ODD, recursively. At the leaf-level, applies LEAF-OPERATION.

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: unit VARIABLE

Returns a BDD node whose HI node is a terminal node of T and LO node is a terminal node of NIL. Useful for representing a boolean variable.

Package

trivialib.bdd

Source

3.bdd.lisp (file)

Function: zdd ROOT &optional VARIABLES NODE-CACHE

Shortcut for instantiating an ODD using ZDD-APPLY.

Package

trivialib.bdd

Source

4.zdd.lisp (file)

Function: zdd-apply F G OP-LEAF

APPLY rule for ZDD.

Package

trivialib.bdd

Source

4.zdd.lisp (file)

Function: zdd-node VARIABLE HI LO

Node generation & pruning rule for ZDD.

Package

trivialib.bdd

Source

4.zdd.lisp (file)

5.1.3 Structures

Structure: leaf ()

Leaf node of a decision diagram

Package

trivialib.bdd

Source

1.struct.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots

Slot: content

Readers

leaf-content (function)

Writers

(setf leaf-content) (function)

Structure: node ()

lightweight node in Decision Diagram.
VARIABLE: an integer representing the index of a variable. cf. VARIABLES slot in structure DD HI,LO: hi/lo pointer

Package

trivialib.bdd

Source

1.struct.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots

Slot: variable

Type

fixnum

Initform

0

Readers

node-variable (function)

Writers

(setf node-variable) (function)

Slot: hi

Type

(or trivialib.bdd:node trivialib.bdd:leaf)

Initform

(trivialib.bdd:leaf nil)

Readers

node-hi (function)

Writers

(setf node-hi) (function)

Slot: lo

Type

(or trivialib.bdd:node trivialib.bdd:leaf)

Initform

(trivialib.bdd:leaf nil)

Readers

node-lo (function)

Writers

(setf node-lo) (function)

Structure: odd ()

Structure representing a whole Decision Diagram.
Holds the context information such as variables and node-cache. For different variable ordering, ODDs are incompatible.

Package

trivialib.bdd

Source

2.odd.lisp (file)

Direct superclasses

structure-object (structure)

Direct slots

Slot: root

Type

(or trivialib.bdd:node trivialib.bdd:leaf)

Initform

(trivialib.bdd:leaf nil)

Readers

odd-root (function)

Writers

(setf odd-root) (function)

Slot: variables

Type

sequence

Initform

trivialib.bdd::*variables*

Readers

odd-variables (function)

Writers

(setf odd-variables) (function)

Slot: node-cache

Type

hash-table

Initform

trivialib.bdd::*node-cache*

Readers

odd-node-cache (function)

Writers

(setf odd-node-cache) (function)

Slot: operation

Type

(function ((or trivialib.bdd:node trivialib.bdd:leaf) (or trivialib.bdd:node trivialib.bdd:leaf) (function (* *) *)) (or trivialib.bdd:node trivialib.bdd:leaf))

Initform

trivialib.bdd::*operation*

Readers

odd-operation (function)

Writers

(setf odd-operation) (function)

5.2 Internal definitions

5.2.1 Special variables

Special Variable: *leaf-cache*

hash table to look up a leaf node of a thing.

Package

trivialib.bdd

Source

1.struct.lisp (file)

Special Variable: *node-cache*

Hash table to look up in order to avoid the creation of redundunt nodes.
This cache is specific to the ODD context defined by the pair of variables and operation(BDD-APPLY or ZDD-APPLY).

Package

trivialib.bdd

Source

1.struct.lisp (file)

Special Variable: *operation*

Generic operations for a decision diagram in the current context, either #’BDD-APPLY or #’ZDD-APPLY.

Package

trivialib.bdd

Source

2.odd.lisp (file)

Special Variable: *variables*

ODD variables in the current context.

Package

trivialib.bdd

Source

1.struct.lisp (file)

5.2.2 Functions

Function: copy-leaf INSTANCE

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: copy-node INSTANCE

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: copy-odd INSTANCE

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: leaf-content INSTANCE

Function: (setf leaf-content) VALUE INSTANCE

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: leaf-p OBJECT

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: make-leaf &key (CONTENT CONTENT)

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: make-node &key (VARIABLE VARIABLE) (HI HI) (LO LO)

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: make-odd &key ROOT VARIABLES NODE-CACHE OPERATION

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: node-hi INSTANCE

Function: (setf node-hi) VALUE INSTANCE

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: node-lo INSTANCE

Function: (setf node-lo) VALUE INSTANCE

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: node-p OBJECT

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: node-variable INSTANCE

Function: (setf node-variable) VALUE INSTANCE

Package

trivialib.bdd

Source

1.struct.lisp (file)

Function: odd-compatible-p ODD1 ODD2

Check if two ODDs have the same variable ordering, node-cache, and operations.

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: odd-node-cache INSTANCE

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: odd-operation INSTANCE

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: odd-p OBJECT

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: odd-root INSTANCE

Package

trivialib.bdd

Source

2.odd.lisp (file)

Function: odd-variables INSTANCE

Package

trivialib.bdd

Source

2.odd.lisp (file)

Appendix A Indexes

A.1 Concepts

A.2 Functions

A.3 Variables

A.4 Data types