Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Visibly pushdown languages properly generalize regular languages and are properly contained in deterministic context-free languages. The complexity of their membership problem is equivalent to that of regular languages. Hover, the corresponding counting problem - computing the number of accepting paths in a visibly pushdown automaton - could be harder than counting paths in a non-deterministic finite automaton: it is only known to be in LogDCFL.#R##N##R##N# investigate the membership and counting problems for generalizations of visibly pushdown automata, defined using the notion of height-determinism.  show that, when the stack-height of a given pushdown automaton can be computed using a finite transducer, both problems have the same complexity as for visibly pushdown languages.  also show that when allowing pushdown transducers instead of finite-state ones, both problems become LogDCFL-complete; this uses the fact that pushdown transducers are sufficient to compute the stack heights of all real-time height-deterministic pushdown automata, and yields a candidate arithmetization of LogDCFL that is no harder than LogDCFL (our main result).
['Nutan Limaye', 'Meena Mahajan', 'Antoine Meyer']
I am writing a research paper on a idea On the complexity of membership and counting in height-deterministic pushdown automata
[{"from": "human", "value": "I am writing a research paper on a idea On the complexity of membership and counting in height-deterministic pushdown automata"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Visibly pushdown languages properly generalize regular languages and are properly contained in deterministic context-free languages. The complexity of their membership problem is equivalent to that of regular languages. Hover, the corresponding counting problem - computing the number of accepting paths in a visibly pushdown automaton - could be harder than counting paths in a non-deterministic finite automaton: it is only known to be in LogDCFL.#R##N##R##N# investigate the membership and counting problems for generalizations of visibly pushdown automata, defined using the notion of height-determinism.  show that, when the stack-height of a given pushdown automaton can be computed using a finite transducer, both problems have the same complexity as for visibly pushdown languages.  also show that when allowing pushdown transducers instead of finite-state ones, both problems become LogDCFL-complete; this uses the fact that pushdown transducers are sufficient to compute the stack heights of all real-time height-deterministic pushdown automata, and yields a candidate arithmetization of LogDCFL that is no harder than LogDCFL (our main result)."}]