software engr who dabbles in theory, sometimes aggressively. career in IT as developer. corporate day job in enterprise java for many years. enjoy the beauty of theory & the excitement of it meeting “killer apps” in the Real World™, and the intense challenge of its premier open problems.
over the years have worked on various homegrown computational complexity projects (since early 1990s) & hope to hear from/ converse with anyone knowledgeable on these subjs, looking esp for feedback via the blog comments! but on other hand dont feel like you have to be an expert to comment here, all constructive comments very much appreciated.
have mainly used a very empirical/experimental approach toward computational complexity theory which feel is underutilized and downplayed in the field for a variety of reasons, some plausible but others specious.
- P vs NP
- have been studying/attacking this problem intermittently, sometimes strongly. shortly before starting this blog, came up with an idea/outline for a NP vs P/Poly proof via monotone circuits, seeking expert feedback.
- theorem proving via actual constructed Turing machines
- built a sophisticated TM compiler and large TMs for attacking automated theorem proving related areas eg extracting special cases of undecidable problems. built a machine for verifying commutative law of addition. modelled the Collatz conjecture. investigate boundary of decidable vs undecidable problems, research into automated theorem proving.
- satisfiability (CNF) problem solver
- looked at optimization heuristics for Davis Putnam related solvers, conversion to DNF etcetera. transition point. esp interested in patterns in clause graphs. code to generate factoring instances and analyze its SAT instance structure