State Elimination Ordering Strategies: Some Experimental Results

Recently, the problem of obtaining a short regular expression equivalent to a given finite automaton has been intensively investigated. Algorithms for converting finite automata to regular expressions have an exponential blow-up in the worst-case. To overcome this, simple heuristic methods have been proposed. In this paper we analyse some of the heuristics presented in the literature and propose new ones. We also present some experimental comparative results based on uniform random generated deterministic finite automata.Comment: In Proceedings DCFS 2010, arXiv:1008.127

FAdo and GUItar: tools for automata manipulation and visualization

Abstract. FAdo is an ongoing project which aims to provide a set of tools for symbolic manipulation of formal languages. To allow highlevel programming with complex data structures, easy prototyping of algorithms, and portability (to use in computer grid systems for example), are its main features. Our main motivation is the theoretical and experimental research, but we have also in mind the construction of a pedagogical tool for teaching automata theory and formal languages. For the graphical visualization and interactive manipulation a new interface application, GUItar, is being developed. In this paper, we describe the main components of the FAdo system as well as the basics of the graphical interface and editor, the export/import filters and its generic interface with external systems, such as FAdo.

On the Uniform Random Generation of Determinisitic Partially Ordered Automata using Monte Carlo Techniques

Partially ordered automata are finite automata admitting no simple loops of length greater than or equal to 2. In this paper we show how to randomly and uniformly generate deterministic accessible partially ordered automata using Monte-Carlo techniques

From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity

The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527

A characterization of those automata that structurally generate finite groups

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper

Binary Decision Diagrams: from Tree Compaction to Sampling

Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of each unique subtree. This yields the celebrated and widely used structure called reduced ordered binary decision diagram (ROBDD). We propose to revisit the classical compaction process to give a new way of enumerating ROBDDs of a given size without considering fully expanded trees and the compaction step. Our method also provides an unranking procedure for the set of ROBDDs. As a by-product we get a random uniform and exhaustive sampler for ROBDDs for a given number of variables and size

On the Uniform Random Generation of Determinisitic Partially Ordered Automata using Monte Carlo Techniques

Partially ordered automata are finite automata admitting no simple loops of length greater than or equal to 2. In this paper we show how to randomly and uniformly generate deterministic accessible partially ordered automata using Monte-Carlo techniques

CHARDA: Causal Hybrid Automata Recovery via Dynamic Analysis

We propose and evaluate a new technique for learning hybrid automata automatically by observing the runtime behavior of a dynamical system. Working from a sequence of continuous state values and predicates about the environment, CHARDA recovers the distinct dynamic modes, learns a model for each mode from a given set of templates, and postulates causal guard conditions which trigger transitions between modes. Our main contribution is the use of information-theoretic measures (1)~as a cost function for data segmentation and model selection to penalize over-fitting and (2)~to determine the likely causes of each transition. CHARDA is easily extended with different classes of model templates, fitting methods, or predicates. In our experiments on a complex videogame character, CHARDA successfully discovers a reasonable over-approximation of the character's true behaviors. Our results also compare favorably against recent work in automatically learning probabilistic timed automata in an aircraft domain: CHARDA exactly learns the modes of these simpler automata.Comment: 7 pages, 2 figures. Accepted for IJCAI 201

Learning probability distributions generated by finite-state machines

We review methods for inference of probability distributions generated by probabilistic automata and related models for sequence generation. We focus on methods that can be proved to learn in the inference in the limit and PAC formal models. The methods we review are state merging and state splitting methods for probabilistic deterministic automata and the recently developed spectral method for nondeterministic probabilistic automata. In both cases, we derive them from a high-level algorithm described in terms of the Hankel matrix of the distribution to be learned, given as an oracle, and then describe how to adapt that algorithm to account for the error introduced by a finite sample.Peer ReviewedPostprint (author's final draft

The Combinatorics of Non-determinism

A deep connection exists between the interleaving semantics of concurrent processes and increasingly labelled combinatorial structures. In this paper we further explore this connection by studying the rich combinatorics of partially increasing structures underlying the operator of non-deterministic choice. Following the symbolic method of analytic combinatorics, we study the size of the computation trees induced by typical non-deterministic processes, providing a precise quantitative measure of the so-called "combinatorial explosion" phenomenon. Alternatively, we can see non-deterministic choice as encoding a family of tree-like partial orders. Measuring the (rather large) size of this family on average offers a key witness to the expressiveness of the choice operator. As a practical outcome of our quantitative study, we describe an efficient algorithm for generating computation paths uniformly at random