Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry, automata theory, and spatiotemporal reasoning.  consider semilinear relations over the rationals and the reals. Under this assumption, the computational complexity of the constraint satisfaction problem (CSP) is known for all finite sets containing R + = { ( x , y , z ) | x + y = z } , ?, and {1}. These problems correspond to expansions of the linear programming feasibility problem.  generalise this result and fully determine the complexity for all finite sets of semilinear relations containing R + . This is accomplished in part by introducing an algorithm, based on computing affine hulls, which solves a new class of semilinear CSPs in polynomial time.  further analyse the complexity of linear optimisation over the solution set and the existence of integer solutions. Constraint satisfaction with semilinear relations and addition is in P or is NP-hard. present an algorithm for a subfamily of problems based on computing affine hulls.Linear optimisation is often polynomial-time equivalent to the decision problem. characterise those problems where integer feasibility equals rational feasibility.
['Peter Jonsson', 'Johan Thapper']
I am writing a research paper on a idea Constraint satisfaction and semilinear expansions of addition over the rationals and the reals
[{"from": "human", "value": "I am writing a research paper on a idea Constraint satisfaction and semilinear expansions of addition over the rationals and the reals"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry, automata theory, and spatiotemporal reasoning.  consider semilinear relations over the rationals and the reals. Under this assumption, the computational complexity of the constraint satisfaction problem (CSP) is known for all finite sets containing R + = { ( x , y , z ) | x + y = z } , ?, and {1}. These problems correspond to expansions of the linear programming feasibility problem.  generalise this result and fully determine the complexity for all finite sets of semilinear relations containing R + . This is accomplished in part by introducing an algorithm, based on computing affine hulls, which solves a new class of semilinear CSPs in polynomial time.  further analyse the complexity of linear optimisation over the solution set and the existence of integer solutions. Constraint satisfaction with semilinear relations and addition is in P or is NP-hard. present an algorithm for a subfamily of problems based on computing affine hulls.Linear optimisation is often polynomial-time equivalent to the decision problem. characterise those problems where integer feasibility equals rational feasibility."}]