A Predicate-Based Model for Computation over State Spaces

Abstract: Many mainstream programming interfaces represent computation procedurally, as sequences of instructions, control-flow constructs, and explicit execution steps. However, several important classes of problems are more naturally described declaratively: one specifies the set of candidate states and the condition that makes a state valid. This paper formalizes a predicate-based abstraction for computation over state spaces. A computational problem is represented by a state space S and a predicate C: S -> {0,1}. Solutions are the states that satisfy the predicate, while execution is delegated to a realization strategy for evaluating, sampling, searching, or otherwise characterizing this solution set. We introduce a minimal semantic-preservation contract that distinguishes the problem specification from backend-specific evaluators and establishes when composed predicates preserve their meaning across realizations. The contribution is a unifying abstraction and preservation contract, rather than a new class of constraint problems or a claim that predicate evaluation is always efficient. Procedural algorithms, solvers, probabilistic methods, and quantum oracles are treated as possible realizations of the same semantic specification. The model is related to constraint satisfaction, satisfiability, logic programming, relational query processing, model checking, high-level quantum languages, and quantum intermediate representations. Its relevance to quantum computation follows from the fact that a Boolean predicate can be materialized, when finite and efficiently representable, as a reversible or phase oracle over computational basis states. This makes the abstraction a bridge between declarative problem specification and quantum-oriented execution without requiring the problem itself to be stated as a circuit.