Problemomis

Problemomis is a theoretical concept introduced in the field of computational complexity in the early 2020s. It refers to a class of decision problems that exhibit both elements of decidability and inherent paradoxical constraints, making them impossible to resolve using standard algorithmic approaches. The term was coined by Dr. Ananya Patel in her paper "On the Limits of Provable Computation," in which she observed that certain problems behave like the liar paradox when formalized in formal logic systems.

Unlike NP‑hard problems, which are known to lack polynomial‑time solutions unless P equals NP, problemomis are characterized by a dual nature: they can be expressed within a decidable formal system, yet any attempt to construct a comprehensive algorithm inevitably encounters self‑referential contradictions. The construction of a problemomis typically involves a recursive definition that forces the algorithm to evaluate its own correctness as part of its input, leading to an infinite regress.

Research on problemomis has implications for both theoretical computer science and philosophy of mathematics. In particular, they challenge conventional notions of decidability and suggest that some forms of reasoning may resist algorithmic encapsulation. A number of researchers, including scholars in formal epistemology, have drawn parallels between problemomis and Gödelian incompleteness, arguing that these problems represent a new class of semi‑incompleteness within algorithmic systems.

Despite their theoretical intrigue, problemomis remain largely unexplored in practical terms, as no computational tasks outside laboratory theory have been shown to fall into this category. Nonetheless, they serve as a valuable counterexample in discussions about the limits of computation and the nature of mathematical truth.