Determination of Logic Reversibility in Reduced Ordered Binary Decision Diagrams Zakaria Hamza CS6805: Logic Synthesis Final Project Professor: Dr. Gerhard Dueck

Outline Achieved Goals Achieved Goals Milestones of Project Milestones of Project Outstanding Issues Outstanding Issues Results Results Logic Synthesis Algorithm Logic Synthesis Algorithm Discussions and Conclusion Discussions and Conclusion Zakaria Hamza CS6805: Logic Synthesis Final Project

Achieved Goals Determination of basic function properties: Determination of basic function properties: Tautological Tautological Reversible Reversible Contradictory Contradictory Module-based interpreter included for function development Module-based interpreter included for function development Ability to map to and from PLA and SPEC files directly Ability to map to and from PLA and SPEC files directly BDD graph generation BDD graph generation Zakaria Hamza CS6805: Logic Synthesis Final Project

Achieved Goals Demonstration of the logic synthesis algorithm: Demonstration of the logic synthesis algorithm: Detect input type Detect input type Use fastest algorithm to derive properties of a binary function and output Use fastest algorithm to derive properties of a binary function and output 1 st image: sample dual variable ROBDD 1 st image: sample dual variable ROBDD 2 nd image: sample truth table derived from specification and PLA file. 2 nd image: sample truth table derived from specification and PLA file. Zakaria Hamza CS6805: Logic Synthesis Final Project

Milestones of Project Zakaria Hamza CS6805: Logic Synthesis Final Project : Pending : Completed

Outstanding Issues Generate reversible functions from logic function specifications Generate reversible functions from logic function specifications Determine if patterns are found within functions: Determine if patterns are found within functions: Transitivity Transitivity Symmetry Symmetry Simplification patterns Simplification patterns Decide best option to analyze any given PLA/SPEC configuration Decide best option to analyze any given PLA/SPEC configuration Optimize incompletely specified functions Optimize incompletely specified functions Zakaria Hamza CS6805: Logic Synthesis Final Project

Results (Runtime) Java-Based Logic Engine: Java-Based Logic Engine: Cross-platform (requires or newer) Cross-platform (requires or newer) Compatible with UNIX command line based packages (i.e.: CUDD) Compatible with UNIX command line based packages (i.e.: CUDD) Includes powerful source code for handling BDD structures using JDD Includes powerful source code for handling BDD structures using JDD Relies on a virtual machine and does not drivers or platform specific features Relies on a virtual machine and does not drivers or platform specific features Uses system calls if available Uses system calls if available Zakaria Hamza CS6805: Logic Synthesis Final Project

Results (Toolbox) Includes C and POSIX command line verification programs Includes C and POSIX command line verification programs PLA and SPEC interchangeability PLA and SPEC interchangeability Programmed adaptability to GraphViz based graph data structures (for large numbers of variables) Programmed adaptability to GraphViz based graph data structures (for large numbers of variables) Supports modifying logic functions Supports modifying logic functions Determines if a function is reversible or could be made reversible using an exponential algorithm Determines if a function is reversible or could be made reversible using an exponential algorithm Zakaria Hamza CS6805: Logic Synthesis Final Project

Results (GUI) Planned support for modification of Karnaugh maps, Toffoli networks, BDD and other logic display formalisms Planned support for modification of Karnaugh maps, Toffoli networks, BDD and other logic display formalisms Allow user input and interaction with display formalism structures Allow user input and interaction with display formalism structures UI engine used to define customizable operations and functions UI engine used to define customizable operations and functions Toolbox is integrated with UI Toolbox is integrated with UI Zakaria Hamza CS6805: Logic Synthesis Final Project

Logic Synthesis Algorithm Input PLA/SPEC/BDD data structures Input PLA/SPEC/BDD data structures Use dynamic programming to analyze function and generate as much information about it as possible Use dynamic programming to analyze function and generate as much information about it as possible Module section for specific functionality Module section for specific functionality Reversibility Reversibility Simplification/Reduction Simplification/Reduction Contradiction Contradiction Quine-McCluskey/SAT/Circuit optional (brute force) algorithms, etc. Quine-McCluskey/SAT/Circuit optional (brute force) algorithms, etc. Create BDD Create BDD Convert to ROBDD Convert to ROBDD User interface manual specifications (inherited functions from Quiver/RevLib as well) User interface manual specifications (inherited functions from Quiver/RevLib as well) Heuristic algorithm to generate output function or graph Heuristic algorithm to generate output function or graph Zakaria Hamza CS6805: Logic Synthesis Final Project

Further Works Resolve outstanding issues (further developing a thesis base) Resolve outstanding issues (further developing a thesis base) Optimize code for better performance and increased range of operability Optimize code for better performance and increased range of operability Use sparse matrices to store truth tables Use sparse matrices to store truth tables Optimize algorithm runtime for large numbers of variables (>20) or use hardware with larger addressing modes Optimize algorithm runtime for large numbers of variables (>20) or use hardware with larger addressing modes Zakaria Hamza CS6805: Logic Synthesis Final Project

Discussions and Conclusions Current algorithm consumes exponential resources relative to the number of input variables Current algorithm consumes exponential resources relative to the number of input variables Functions may or may not terminate depending on how effectively virtual memory is used Functions may or may not terminate depending on how effectively virtual memory is used Storing large truth tables is simply infeasible and a graph structure is almost indispensable Storing large truth tables is simply infeasible and a graph structure is almost indispensable Tree-based compression structures may reduce runtime dramatically if properly encoded Tree-based compression structures may reduce runtime dramatically if properly encoded Zakaria Hamza CS6805: Logic Synthesis Final Project