Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property—nondeterminism—in nondeterministic finite automata has not been well embodied in the generalization. In this paper, we introduce nondeterministic fuzzy automata with or without -moves and fuzzy languages recognized by them. Furthermor...

A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various degrees of decomposability between undecomposable and perfectly decomposable are shown to exist.

We investigate the state complexity of multiple unions and of multiple intersections for prefix-free regular languages. Prefix-free deterministic finite automata have their own unique structural properties that are crucial for obtaining state complexity upper bounds that are improved from those for general regular languages. We present a tight lower bound construction for k-union using an alpha...

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class including groups, such an automaton accepts the word problem of a group H if and only if H has a finite index subgroup which embeds in M . In the case that M is...

Weighted automata and transducers are powerful devices used in many large-scale applications. The efficiency of these applications is substantially increased when the automata or transducers used are deterministic. There exists a general determinization algorithm for weighted automata and transducers that is an extension of the classical subset construction used in the case of unweighted finite...

In this paper, we formulate, analyze, and devise methodologies to verify the notion of infinite-step opacity in discrete event systems that are modeled as (possibly non-deterministic) finite automata with partial observation on their transitions. Specifically, a system is infinitestep opaque if the entrance of the system state at any particular instant to a set of secret states remains opaque (...

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability just of a certain explicit family of groups (“Mother groups”) which is done by analyzing the asymptotic properties of random walks on these groups.

This work treats the problem of error-resilient DNA searching via oblivious evaluation of finite automata, formulated as follows: a client has a DNA sequence, and a service provider has a pattern that corresponds to a genetic test. Error-resilient searching can be achieved by representing the pattern as a finite automata and evaluating it on the DNA sequence, which is treated as the input to th...

This problem arose f rom an a t t empt to make a general s tudy of reliability iii :cbinputerlike machines. The classic results 0f:von Neumann (yon Neumgnn; 19o6) deal only with networks which do not have any feedback. Thus a malfunction only causes the network to be in the incorrect State for a fixed length of t i m e . However ; a malfunction in the general case with feedback can cause an err...

We present an algorithm that eliminates complex role inclusion axioms (RIAs) from a SROIQ ontology preserving all logical consequences not involving non-simple roles. Unlike other existing methods, our algorithm does not explicitly construct finite automata recognizing the languages generated by the RIAs. Instead, it is formulated as a recursive expansion of universal restrictions, similar to w...