Related papers: The state complexity of a class of operations invo…
Monsters and modifiers are two concepts recently developed in the state complexity theory. A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions…
A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of functions allowing one to transform a set of automata into one automaton. We revisit some language…
Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or…
The state complexity of the result of a regular operation is often positively correlated with the number of distinct transformations induced by letters in the minimal deterministic finite automaton of the input languages. That is, more…
In this paper we consider the state complexity of an operation on formal languages, root(L). This naturally entails the discussion of the monoid of transformations of a finite set. We obtain good upper and lower bounds on the state…
We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language -- which is the number of its (left) quotients, and…
The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
We investigate the state complexity of the star of symmetrical differences using modifiers and monsters. A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of…
The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most…
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model…
The quotient complexity, also known as state complexity, of a regular language is the number of distinct left quotients of the language. The quotient complexity of an operation is the maximal quotient complexity of the language resulting…
Most of the computational study of election problems has assumed that each voter's preferences are, or should be extended to, a total order. However in practice voters may have preferences with ties. We study the complexity of manipulative…
The quotient complexity of a regular language L is the number of left quotients of L, which is the same as the state complexity of L. Suppose that L and L' are binary regular languages with quotient complexities m and n, and that the…
The state complexity of basic operations on finite languages (considering complete DFAs) has been in studied the literature. In this paper we study the incomplete (deterministic) state and transition complexity on finite languages of…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
We study the complexity of basic regular operations on languages represented by incomplete deterministic or nondeterministic automata, in which all states are final. Such languages are known to be prefix-closed. We get tight bounds on both…
It is important to study how strategic agents can affect the outcome of an election. There has been a long line of research in the computational study of elections on the complexity of manipulative actions such as manipulation and bribery.…
Given an order of the underlying alphabet we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one \emph{and}…
For a robot to be perfect and enter the everyday life of humans,like computers did, it needs to move from special-purpose robots to general-purpose. So, the idea of modularity is considered in this project.Thus, any type of task that falls…