Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theory of linear arithmetic (TLA), also known as the Theory of Rationals, is an extremely ll-studied theory. It has been widely applied to a number of domains, including program verification and constraint specification.  discusses the computational complexities of two broad fragments of TLA, namely Quantified Linear Programs (QLPs) and Quantified Linear Implications (QLIs). These fragments are ideal for expressing specifications in real-time scheduling, and for modeling reactive systems. ,  study the computational complexities of several variants of QLPs and QLIs. Our principal result shows that there exists a one-to-one correspondence beten alternations in a class of QLIs and the complexity classes comprising the polynomial hierarchy PH. In other words, for each class of the PH, there exists a class of QLIs that is complete for that class. Our work mirrors the work in [L.J. Stockmeyer, The Polynomial-Time Hierarchy, Theoretical Computer Science, 3:1-22, 1977] which established the connection beten the classes of PH and quantifier alternations in a Quantified Boolean Formula. Our results are surprising, since the variables in the fragments that  consider are continuous, as opposed to discrete.
['Piotr J. Wojciechowski', 'Pavlos Eirinakis', 'K. Subramani']
I am writing a research paper on a idea Analyzing restricted fragments of the theory of linear arithmetic
[{"from": "human", "value": "I am writing a research paper on a idea Analyzing restricted fragments of the theory of linear arithmetic"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The theory of linear arithmetic (TLA), also known as the Theory of Rationals, is an extremely ll-studied theory. It has been widely applied to a number of domains, including program verification and constraint specification.  discusses the computational complexities of two broad fragments of TLA, namely Quantified Linear Programs (QLPs) and Quantified Linear Implications (QLIs). These fragments are ideal for expressing specifications in real-time scheduling, and for modeling reactive systems. ,  study the computational complexities of several variants of QLPs and QLIs. Our principal result shows that there exists a one-to-one correspondence beten alternations in a class of QLIs and the complexity classes comprising the polynomial hierarchy PH. In other words, for each class of the PH, there exists a class of QLIs that is complete for that class. Our work mirrors the work in [L.J. Stockmeyer, The Polynomial-Time Hierarchy, Theoretical Computer Science, 3:1-22, 1977] which established the connection beten the classes of PH and quantifier alternations in a Quantified Boolean Formula. Our results are surprising, since the variables in the fragments that  consider are continuous, as opposed to discrete."}]