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Foundational Background
NDP originates in the relation between syntax, semantics, and state representation. A Boolean function may be written syntactically as a formula while its semantics is determined by the assignments under which that formula evaluates. Binary Decision Diagrams (BDDs) provide a graph representation of Boolean functions in which equivalent continuations can be represented by shared residual structure rather than repeatedly enumerated.
The NDP research line develops this observation through a constructive approach to residual-state representation. Its historical starting point was the study of Classical Arabic, where semantic distinctions are systematically carried by internal symbolic structure and permutations rather than being determined by context alone. Transferred to Boolean representation, this motivated the investigation of whether apparently syntactic variable structures encode regularities that permit computationally useful semantic organization.
Applied to SAT/CNF processing, this led to the NDP approach of organizing variables and residual clause states so that equivalent computational continuations can be identified and represented without retaining their complete syntactic histories. BDDs provide the executable representation, while the underlying issue is more general: which distinctions in a computational state carry information required for all future responses, and which distinctions can be discarded?
This question subsequently becomes explicit in Constraint Physical Computing (CPC). CPC separates state identity, quotient representation, exact semantic carriers, realization, dynamics, readout, and resource requirements, providing the formal setting in which claims about computational representation and physical implementation can be stated and independently tested.
For the mathematical development track, the Arabic-language connection, BDD results, and subsequent CPC formalization, see Foundational Papers and Constraint Physical Computing on Resources.
NDP originates in the relation between syntax, semantics, and state representation. A Boolean function may be written syntactically as a formula while its semantics is determined by the assignments under which that formula evaluates. Binary Decision Diagrams (BDDs) provide a graph representation of Boolean functions in which equivalent continuations can be represented by shared residual structure rather than repeatedly enumerated.
The NDP research line develops this observation through a constructive approach to residual-state representation. Its historical starting point was the study of Classical Arabic, where semantic distinctions are systematically carried by internal symbolic structure and permutations rather than being determined by context alone. Transferred to Boolean representation, this motivated the investigation of whether apparently syntactic variable structures encode regularities that permit computationally useful semantic organization.
Applied to SAT/CNF processing, this led to the NDP approach of organizing variables and residual clause states so that equivalent computational continuations can be identified and represented without retaining their complete syntactic histories. BDDs provide the executable representation, while the underlying issue is more general: which distinctions in a computational state carry information required for all future responses, and which distinctions can be discarded?
This question subsequently becomes explicit in Constraint Physical Computing (CPC). CPC separates state identity, quotient representation, exact semantic carriers, realization, dynamics, readout, and resource requirements, providing the formal setting in which claims about computational representation and physical implementation can be stated and independently tested.
For the mathematical development track, the Arabic-language connection, BDD results, and subsequent CPC formalization, see Foundational Papers and Constraint Physical Computing on Resources.
Constraint Physical Computing — CPC Validation
GitHub — source and current development
Zenodo — CPC Validation v0.6.0
CPC Zenodo Community
NDP 5.6.7 bare-metal (GitHub 2025-MAR-12) featuring:
- C++ implementation
- OpenMPI multiprocessing
- distributed cluster execution
- FACT processing
- README and build instructions
- source-level implementation of the residual-state machinery
README included in NDP-5.6.7
LICENSE
NDP-5.6.7
ClauseSetPool.hpp for NDP-5.6.7
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