An Improved Construction of Deterministic Omega-automaton using Derivatives

Abstract. In an earlier paper, the author used derivatives to construct a deterministic automaton recognizing the language defined by an ω-regular expression. The construction was related to a determinization method invented by Safra. This paper describes a new construction, inspired by Piterman's improvement to Safra's method. It produces an automaton with fewer states. In addition, the presentation and proofs are simplified by going via a nondeterministic automaton having derivatives as states

Left Recursion in Parsing Expression Grammars

Parsing Expression Grammars (PEGs) are a formalism that can describe all deterministic context-free languages through a set of rules that specify a top-down parser for some language. PEGs are easy to use, and there are efficient implementations of PEG libraries in several programming languages. A frequently missed feature of PEGs is left recursion, which is commonly used in Context-Free Grammars (CFGs) to encode left-associative operations. We present a simple conservative extension to the semantics of PEGs that gives useful meaning to direct and indirect left-recursive rules, and show that our extensions make it easy to express left-recursive idioms from CFGs in PEGs, with similar results. We prove the conservativeness of these extensions, and also prove that they work with any left-recursive PEG. PEGs can also be compiled to programs in a low-level parsing machine. We present an extension to the semantics of the operations of this parsing machine that let it interpret left-recursive PEGs, and prove that this extension is correct with regards to our semantics for left-recursive PEGs.Comment: Extended version of the paper "Left Recursion in Parsing Expression Grammars", that was published on 2012 Brazilian Symposium on Programming Language

TRX: A Formally Verified Parser Interpreter

Parsing is an important problem in computer science and yet surprisingly little attention has been devoted to its formal verification. In this paper, we present TRX: a parser interpreter formally developed in the proof assistant Coq, capable of producing formally correct parsers. We are using parsing expression grammars (PEGs), a formalism essentially representing recursive descent parsing, which we consider an attractive alternative to context-free grammars (CFGs). From this formalization we can extract a parser for an arbitrary PEG grammar with the warranty of total correctness, i.e., the resulting parser is terminating and correct with respect to its grammar and the semantics of PEGs; both properties formally proven in Coq.Comment: 26 pages, LMC

From LTL and Limit-Deterministic B\"uchi Automata to Deterministic Parity Automata

Controller synthesis for general linear temporal logic (LTL) objectives is a challenging task. The standard approach involves translating the LTL objective into a deterministic parity automaton (DPA) by means of the Safra-Piterman construction. One of the challenges is the size of the DPA, which often grows very fast in practice, and can reach double exponential size in the length of the LTL formula. In this paper we describe a single exponential translation from limit-deterministic B\"uchi automata (LDBA) to DPA, and show that it can be concatenated with a recent efficient translation from LTL to LDBA to yield a double exponential, \enquote{Safraless} LTL-to-DPA construction. We also report on an implementation, a comparison with the SPOT library, and performance on several sets of formulas, including instances from the 2016 SyntComp competition

Topologies Refining the Cantor Topology on X ω

International audienceThe space of one-sided infinite words plays a crucial rôle in several parts of Theoretical Computer Science. Usually, it is convenient to regard this space as a metric space, the Cantor-space. It turned out that for several purposes topologies other than the one of the Cantor-space are useful, e.g. for studying fragments of first-order logic over infinite words or for a topological characterisation of random infinite words. It is shown that both of these topologies refine the topology of the Cantor-space. Moreover, from common features of these topologies we extract properties which characterise a large class of topologies. It turns out that, for this general class of topologies, the corresponding closure and interior operators respect the shift operations and also, to some respect, the definability of sets of infinite words by finite automata

Construction of a Deterministic

A deterministic automaton recognizing a given ω-regular language is constructed from an ω-regular expression with the help of derivatives. The construction is related to Safra's algorithm, in about the same way as the classical derivative method is related to the subset construction