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

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

LTLf and LDLf Monitoring: A Technical Report

Runtime monitoring is one of the central tasks to provide operational decision support to running business processes, and check on-the-fly whether they comply with constraints and rules. We study runtime monitoring of properties expressed in LTL on finite traces (LTLf) and in its extension LDLf. LDLf is a powerful logic that captures all monadic second order logic on finite traces, which is obtained by combining regular expressions and LTLf, adopting the syntax of propositional dynamic logic (PDL). Interestingly, in spite of its greater expressivity, LDLf has exactly the same computational complexity of LTLf. We show that LDLf is able to capture, in the logic itself, not only the constraints to be monitored, but also the de-facto standard RV-LTL monitors. This makes it possible to declaratively capture monitoring metaconstraints, and check them by relying on usual logical services instead of ad-hoc algorithms. This, in turn, enables to flexibly monitor constraints depending on the monitoring state of other constraints, e.g., "compensation" constraints that are only checked when others are detected to be violated. In addition, we devise a direct translation of LDLf formulas into nondeterministic automata, avoiding to detour to Buechi automata or alternating automata, and we use it to implement a monitoring plug-in for the PROM suite

Noncooperative algorithms in self-assembly

We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar non-cooperative variant of Winfree's abstract Tile Assembly Model. This model has been the center of several open problems and conjectures in the last fifteen years, and the first fully general results on its computational power were only proven recently (SODA 2014). These results, as well as ours, exemplify the intricate connections between computation and geometry that can occur in self-assembly. In this model, tiles can stick to an existing assembly as soon as one of their sides matches the existing assembly. This feature contrasts with the general cooperative model, where it can be required that tiles match on \emph{several} of their sides in order to bind. In order to describe our algorithms, we also introduce a generalization of regular expressions called Baggins expressions. Finally, we compare this model to other automata-theoretic models.Comment: A few bug fixes and typo correction

Tuning the program transformers from LCC to PDL

ISBN del número: 978-1-84890-274-9This work proposes an alternative definition of the so-called program transformers used to obtain reduction axioms in the Logic of Communication and Change (LCC). Our proposal uses an elegant matrix treatment of Brzozowski’s equational method instead of Kleene’s translation from finite automata to regular expressions. The two alternatives are shown to be equivalent, with Brzozowski’s method having the advantage of generating smaller expressions for models with average connectivity

Tuning the program transformers from LCC to PDL

This work proposes an alternative definition of the so-called program transformers used to obtain reduction axioms in the Logic of Communication and Change (LCC). Our proposal uses an elegant matrix treatment of Brzozowski’s equational method instead of Kleene’s translation from finite automata to regular expressions. The two alternatives are shown to be equivalent, with Brzozowski’s method having the advantage of generating smaller expressions for models with average connectivity

Compositional Verification for Timed Systems Based on Automatic Invariant Generation

We propose a method for compositional verification to address the state space explosion problem inherent to model-checking timed systems with a large number of components. The main challenge is to obtain pertinent global timing constraints from the timings in the components alone. To this end, we make use of auxiliary clocks to automatically generate new invariants which capture the constraints induced by the synchronisations between components. The method has been implemented in the RTD-Finder tool and successfully experimented on several benchmarks

Complexity Hierarchies Beyond Elementary

We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary complexity, which occur naturally in logic, combinatorics, formal languages, verification, etc., with complexities ranging from simple towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep updating the catalogue of problems from Section 6 in future revision