Formal languages defined by uniform substitutions

Regularity of Languages Defined by Formal Series with Isolated Cut Point

Explicit Substitutions and Programming Languages

The λ-calculus has been much used to study the theory of substitution in logical systems and programming languages. However, with explicit substitutions, it is possible to get finer properties with respect to gradual implementations of substitutions as effectively done in runtimes of programming languages. But the theory of explicit substitutions has some defects such as non-confluence or the n...

Languages under substitutions and balanced

= zu2(i + k) for all i E I,. If I = Z we call w a Z-word or a bi-infinite word. If I is finite we call x finite and its length Ixl is defined as The usual notation for a finite word of length n is x = xi ... zn where all xi E {a, &}. We write {a, b}* for the collection of finite words and {a, b~+ for the nonempty finite words. (The empty word will be denoted throughout by e). The concatena...

Quantitative Languages Defined by Functional Automata

A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures. Furthermore, the...

Congruences Defined by Languages and Filters

The usual right congruence :"L can be generalized in the following manner: x ~£: ,LY :¢> {z t xz e L ~:~yz eL} ~,LP, where ~9 ° is a family of languages. It turns out to be useful when £# is a falter with an additional property. Furthermore semifilters are introduced and studied. It is also possible to define congruences by filters. Assuming the (right) congruences to have finite index yields a...