Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be vied as nodes in an infinite tree, and transitions beten states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree.  introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems.  demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and  prove a matching lor bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.
['Orna Kupferman', 'Nir Piterman', 'Moshe Y. Vardi']
I am writing a research paper on a idea Model checking linear properties of prefix-recognizable systems
[{"from": "human", "value": "I am writing a research paper on a idea Model checking linear properties of prefix-recognizable systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be vied as nodes in an infinite tree, and transitions beten states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by an alternating two-way automaton that navigates through the tree.  introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems.  demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and  prove a matching lor bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling."}]