🤖 AI Summary
This work addresses the limitations of mainstream procedural programming interfaces in naturally expressing declarative problems defined over state spaces and validity conditions. It proposes a predicate-based computational abstraction that models problems as a state space equipped with Boolean predicates, where solutions correspond to states satisfying the predicate, and execution is delegated to backend strategies. By introducing a unified predicate abstraction and semantics-preserving contracts, the approach decouples problem specification from solver implementation, enabling composable realizations across diverse backends—including constraint solvers, probabilistic inference engines, and quantum oracles—while preserving semantic equivalence. Notably, this framework enables seamless adaptation of declarative problems to quantum execution without requiring manual rewriting into quantum circuits, thereby establishing a general-purpose bridge between high-level problem descriptions and heterogeneous computational backends, including quantum computing platforms.
📝 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.