On Properties and State Complexity of Deterministic State-Partition Automata
نویسندگان
چکیده
A deterministic automaton accepting a regular language L is a state-partition automaton with respect to a projection P if the state set of the deterministic automaton accepting the projected language P (L), obtained by the standard subset construction, forms a partition of the state set of the automaton. In this paper, we study fundamental properties of state-partition automata. We provide a construction of the minimal state-partition automaton for a regular language and a projection, discuss closure properties of state-partition automata under the standard constructions of deterministic automata for regular operations, and show that almost all of them fail to preserve the property of being a statepartition automaton. Finally, we define the notion of a state-partition complexity, and prove the tight bound on the state-partition complexity of regular languages represented by incomplete deterministic automata.
منابع مشابه
Reduction of Computational Complexity in Finite State Automata Explosion of Networked System Diagnosis (RESEARCH NOTE)
This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...
متن کاملDISTINGUISHABILITY AND COMPLETENESS OF CRISP DETERMINISTIC FUZZY AUTOMATA
In this paper, we introduce and study notions like state-\linebreak distinguishability, input-distinguishability and output completeness of states of a crisp deterministic fuzzy automaton. We show that for each crisp deterministic fuzzy automaton there corresponds a unique (up to isomorphism), equivalent distinguished crisp deterministic fuzzy automaton. Finally, we introduce two axioms related...
متن کاملState Complexity Advantages of Ultrametric Automata
Ultrametric automata have properties similar to the properties of probabilistic automata but the descriptional power of these types of automata can differ very much. In this paper, we compare ultrametric automata with deterministic, nondeterministic, probabilistic and alternating automata with various state complexities. We also show that two-way ultrametric automata can have a smaller state co...
متن کاملState Complexity of Union and Intersection of Finite Languages
We investigate the state complexity of union and intersection for finite languages. Note that the problem of obtaining the tight bounds for both operations was open. First we compute upper bounds using structural properties of minimal deterministic finite-state automata for finite languages. Then, we show that the upper bounds are tight if we have a variable sized alphabet that can depend on th...
متن کاملOperational State Complexity of Deterministic Unranked Tree Automata
We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic tree automata are obtained. For tree concatenation we establish a tight upper bound that is of a different order than the known state complexity of concatenatio...
متن کامل