Topic
Omega-regular language
About: Omega-regular language is a research topic. Over the lifetime, 5 publications have been published within this topic receiving 91 citations.
Papers
11 Aug 2009
TL;DR: It is shown that the set of words with value greater than a threshold can be non-omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated and it is proved that the omega- regular language is robust against small perturbations of the transition weights.
Abstract: Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be non-omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L1 and L2, we consider the operations max(L1, L2), min(L1, L2), and 1-L1, which generalize the boolean operations on languages, as well as the sum L1 + L2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.
59 citations
Journal Article•
2 citations
1 Jan 2015
TL;DR: In this article, a quadratic-time algorithm for computing the syntactic morphism from any given strongly recognizing morphism is given, and the minimization problem is shown to be easy as well.
Abstract: Morphisms to finite semigroups can be used for recognizing omega-regular languages. The so-called strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic morphism) and a trivial complementation procedure. We give a quadratic-time algorithm for computing the syntactic morphism from any given strongly recognizing morphism, thereby showing that minimization is easy as well. In addition, we give algorithms for efficiently solving various decision problems for weakly recognizing morphisms. Weakly recognizing morphism are often smaller than their strongly recognizing counterparts. Finally, we describe the language operations needed for converting formulas in monadic second-order logic (MSO) into strongly recognizing morphisms, and we give some experimental results.
TL;DR: It is shown that all ω -regular languages which are deterministic and co-deterministic are monitorable, but certain deterministic liveness properties like “infinitely many a 's” cannot be written as a countable union of monitorable languages.
TL;DR: An algorithm is described that gets as input an infinite lasso-shape word of the form x ċ yω, for finite words x and y, which returns "yes" if w ∈ L(A), and returns "no" with probability 2/3 if w is e-far from L(B).
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2015 | 1 |
| 2014 | 1 |
| 2009 | 1 |
| 2004 | 1 |
| 2001 | 1 |