Commutative One-counter languages are regular

Learning Commutative Regular Languages

Identifying Regular Languages over Partially-Commutative Monoids

We deene a new technique useful in identifying a subclass of regular languages deened on a free partially commutative monoid (regular trace languages), using equivalence and membership queries. Our algorithm extends an algorithm deened by Dana Angluin in 1987 to learn DFA's. The words of a trace language can be seen as equivalence classes of strings. We show how to extract, from a given equival...

One-Unambiguous Regular Languages

The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic meta-language for the definition of textual markup systems. In the standard, the right-hand sides of productions are based on regular expressions, although only regular expressions that denote words unambiguously, in the sense of the ISO standard, are allowed. In general, a word that is denoted by a regula...

One-Counter Verifiers for Decidable Languages

Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show that if we use architecturally restricted verifiers instead of restricting the working memory, i.e. replacing the working tape(s) with a single counter, we ca...

Toehold DNA Languages are Regular

We explore a method of designing algorithms using two types of DNA strands, namely rule strands (rules) and input strands. Rules are fixed in advance, and their task is to bind with the input strands in order to produce an output. We present algorithms for divisibility and primality testing as well as for square root computation. We measure the complexity of our algorithms in terms of the neces...