Efficient learnability using the state merging algorithm is known for a subclass of probabilistic automata termed μ-distinguishable. In this paper, we prove that state merging algorithms can be extended to efficiently learn a larger class of automata. In particular, we show learnability of a subclass which we call μ2-distinguishable. Using an analog of the Myhill-Nerode theorem for probabilisti...

Rank-width is a structural graph measure introduced by Oum and Seymour and aimed at better handling of graphs of bounded clique-width. We propose a formal framework and tools for easy design of dynamic algorithms running directly on a rank-decomposition of a graph (on contrary to the usual approach which translates a rankdecomposition into a clique-width expression, with a possible exponential ...

Tree transducers are an expressive formalism for reasoning about tree structured data. Practical applications range from XSLT-like document transformations to translations of natural languages. Important problems for transducers are to decide whether two transducers are equivalent, to construct normal forms, give semantic characterizations, and type checking, i.e., to check whether the produced...

Advances in t,he theory of well-partially-ordered sets now make it possible to prove the existence of low-degree polynomial-time decision algorithms for a vast assortment of natural problems, many of which seem to resist more traditional means of complexity classification. Surprisingly, these proofs are nonconstructive, based on the promise of an iiiiknown but finite obstruction set. Recent pro...

We present a formal constructive theory of regular languages consisting of about 1400 lines of Coq/Ssreflect. As representations we consider regular expressions, deterministic and nondeterministic automata, and Myhill and Nerode partitions. We construct computable functions translating between these representations and show that equivalence of representations is decidable. We also establish the...

We present a constructive formalization of the Myhill-Nerode theorem on the minimization of nite automata that follows the account in Hopcroft and Ullman's book Formal Languages and Their Relation to Automata. We chose to formalize this theorem because it illustrates many points critical to formalization of computational mathematics, especially the extraction of an important algorithm from a pr...

Recognizable sets of unranked, unordered trees have been introduced in Courcelle [C89] in a Myhill-Nerode [N58] style of inverse homomorphisms of suitable finite magmas. This is equivalent of being the the union of some congruence classes of a congruence of finite index. We will add to the well-known concept of regular tree grammars a handling of nodes labeled with ǫ. With this rather unconvent...

Rank-width is a rather new structural graph measure introduced by Oum and Seymour in 2003 in order to find an efficiently computable approximation of clique-width of a graph. Being a very nice graph measure indeed, the only serious drawback of rank-width was that it is virtually impossible to use a given rank-decomposition of a graph for running dynamic algorithms on it. We propose a new indepe...

The NuPRL system [3] was designed for interactive writing of machine–checked constructive proofs and for extracting algorithms from the proofs. The extracted algorithms are guaranteed to be correct 1 which makes it possible to use NuPRL as a programming language with built-in verification[1,5,7,8,9,10]. However it turned out that proofs written without algorithmic efficiency in mind often produ...