9 research outputs found
Prefix and Right-Partial Derivative Automata
Recently, Yamamoto presented a new method for the conversion from regular expressions (REs) to non-deterministic finite automata (NFA) based on the Thompson epsilon-NFA (A(T)). The A(T) automaton has two quotients discussed: the suffix automaton A(suf) and the prefix automaton, A(pre). Eliminating epsilon-transitions in A(T), the Glushkov automaton (A(pos)) is obtained. Thus, it is easy to see that A(suf) and the partial derivative automaton (A(pd)) are the same. In this paper, we characterise the A(pre) automaton as a solution of a system of left RE equations and express it as a quotient of A(pos) by a specific left-invariant equivalence relation. We define and characterise the right-partial derivative automaton ((A) over left arrow (pd)). Finally, we study the average size of all these constructions both experimentally and from an analytic combinatorics point of view
Confluent Orthogonal Drawings of Syntax Diagrams
We provide a pipeline for generating syntax diagrams (also called railroad
diagrams) from context free grammars. Syntax diagrams are a graphical
representation of a context free language, which we formalize abstractly as a
set of mutually recursive nondeterministic finite automata and draw by
combining elements from the confluent drawing, layered drawing, and smooth
orthogonal drawing styles. Within our pipeline we introduce several heuristics
that modify the grammar but preserve the language, improving the aesthetics of
the final drawing.Comment: GD 201
Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels
We are interested in regular expressions and transducers that represent word
relations in an alphabet-invariant way---for example, the set of all word pairs
u,v where v is a prefix of u independently of what the alphabet is. Current
software systems of formal language objects do not have a mechanism to define
such objects. We define transducers in which transition labels involve what we
call set specifications, some of which are alphabet invariant. In fact, we give
a more broad definition of automata-type objects, called labelled graphs, where
each transition label can be any string, as long as that string represents a
subset of a certain monoid. Then, the behaviour of the labelled graph is a
subset of that monoid. We do the same for regular expressions. We obtain
extensions of a few classic algorithmic constructions on ordinary regular
expressions and transducers at the broad level of labelled graphs and in such a
way that the computational efficiency of the extended constructions is not
sacrificed. For regular expressions with set specs we obtain the corresponding
partial derivative automata. For transducers with set specs we obtain further
algorithms that can be applied to questions about independent regular
languages, in particular the witness version of the independent property
satisfaction question
Position Automaton Construction for Regular Expressions with Intersection
Positions and derivatives are two essential notions in the conversion methods from regular expressions to equivalent finite automata. Partial derivative based methods have recently been extended to regular expressions with intersection. In this paper, we present a position automaton construction for those expressions. This construction generalizes the notion of position making it compatible with intersection. The resulting automaton is homogeneous and has the partial derivative automaton as its quotient
On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection
Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016
Comparison of construction algorithms for minimal, acyclic, deterministic, finite-state automata from sets of strings
This paper compares various methods for constructing minimal, deterministic, acyclic, finite-state automata (recognizers) from sets of words. Incremental, semi-incremental, and non-incremental methods have been implemented and evaluated
Algorithms for computing finite semigroups
The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set {1,..., n}, or the semigroup of n × n matrices with entries in a given finite semiring. The algorithm produces simultaneously a presentation of the semigroup by generators and relations, a confluent rewriting system for this presentation and the Cayley graph of the semigroup. The elements of the semigroup are identified with the reduced words of the rewriting system. We also give some efficient algorithms to compute the Green relations, the local subsemigroups and the syntactic quasi-order of a subset of the semigroup