Papers on Deniz Duman

Configuration Identity as a Formal Parameter in Deterministic State Counting

Sun, 23 Aug 2026 00:00:00 +0000

Standard models of deterministic computation count configurations as distinct states whenever their concrete encodings differ. The practice is everywhere and is rarely isolated as a formal choice, even though arguments about reachable state-space size and traversal cost are stated relative to it.

This paper treats configuration identity as a parameter. Deterministic transition systems are equipped with an equivalence relation on configurations and a canonical representative map, and computation is then defined over canonical states.

Canonical Quotient-State Realization of Bounded-Width Dynamic Programming in Layered Tseytin 3-CNF

Sun, 23 Aug 2026 00:00:00 +0000

This paper studies canonical quotient-state compression in a deterministic residual decision model, on a bounded-width layered 3-CNF family that arises from standard Tseytin encodings of bounded-fanin layered Boolean circuits. An admitted target family is defined, and the fixed gate-by-gate translation from the source family is shown to land inside it.

On that family the paper proves that every reachable residual admits an active/future cut with bounded boundary; that the unresolved suffix affects continuation only through a Boolean suffix summary on that boundary; that the suffix summary at a fixed cut index is determined by the fixed input and the cut position; that the suffix-summary sequence is computable in deterministic polynomial time by backward dynamic programming on the layered suffix; that the branch-labelled successor on canonical residual states is well defined; and that for fixed width and fanin bound, the reachable canonical quotient-state space is linearly bounded in the clause count.

Exact Semantic Carriers for Structured Physical Systems

Sun, 23 Aug 2026 00:00:00 +0000

Exact search states can be individuated by syntactic history, or by a smaller carrier that preserves exact continuation semantics. This paper gives a sufficient traversal criterion for deterministic polynomial-time computation: exact semantic factorisation, a polynomially bounded reachable carrier image, polynomial-length canonical encodings with efficient equality, complete exact polynomial-time successor dynamics, polynomially bounded progression, and exact readout.

The criterion is deliberately framed as an audit schema for exact dynamic-programming arguments, not as a new complexity mechanism.