Degree of Sequentiality of Weighted Automata

Weighted automata (WA) are an important formalism to describe quantitative properties. Obtaining equivalent deterministic machines is a longstanding research problem. In this paper we consider WA with a set semantics, meaning that the semantics is given by the set of weights of accepting runs. We focus on multi-sequential WA that are defined as finite unions of sequential WA. The problem we address is to minimize the size of this union. We call this minimum the degree of sequentiality of (the relation realized by) the WA. For a given positive integer k, we provide multiple characterizations of relations realized by a union of k sequential WA over an infinitary finitely generated group: a Lipschitz-like machine independent property, a pattern on the automaton (a new twinning property) and a subclass of cost register automata. When possible, we effectively translate a WA into an equivalent union of k sequential WA. We also provide a decision procedure for our twinning property for commutative computable groups thus allowing to compute the degree of sequentiality. Last, we show that these results also hold for word transducers and that the associated decision problem is PSPACE -complete

Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the associated extended expressions called hairpin expressions. More precisely, we extend partial derivation of regular expressions to two-sided partial derivation of hairpin expressions and we show how to deduce a recognizer for a hairpin expression from its two-sided derived term automaton, providing an alternative proof of the fact that hairpin completions of regular languages are linear context-free.Comment: 28 page

Efficient deterministic finite automata split-minimization derived from Brzozowski's algorithm

Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DFA minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft s classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.García Gómez, P.; López Rodríguez, D.; Vázquez-De-Parga Andrade, M. (2014). Efficient deterministic finite automata split-minimization derived from Brzozowski's algorithm. International Journal of Foundations of Computer Science. 25(6):679-696. doi:10.1142/S0129054114500282S679696256Vázquez de Parga, M., García, P., & López, D. (2013). A polynomial double reversal minimization algorithm for deterministic finite automata. Theoretical Computer Science, 487, 17-22. doi:10.1016/j.tcs.2013.03.005Courcelle, B., Niwinski, D., & Podelski, A. (1991). A geometrical view of the determinization and minimization of finite-state automata. Mathematical Systems Theory, 24(1), 117-146. doi:10.1007/bf02090394POLÁK, L. (2005). MINIMALIZATIONS OF NFA USING THE UNIVERSAL AUTOMATON. International Journal of Foundations of Computer Science, 16(05), 999-1010. doi:10.1142/s0129054105003431Gries, D. (1973). Describing an algorithm by Hopcroft. Acta Informatica, 2(2). doi:10.1007/bf00264025Blum, N. (1996). An O(n log n) implementation of the standard method for minimizing n-state finite automata. Information Processing Letters, 57(2), 65-69. doi:10.1016/0020-0190(95)00199-9Knuutila, T. (2001). Re-describing an algorithm by Hopcroft. Theoretical Computer Science, 250(1-2), 333-363. doi:10.1016/s0304-3975(99)00150-

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.

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

Understanding mixed sequence DNA recognition by novel designed compounds: the kinetic and thermodynamic behavior of azabenzimidazole diamidines

Sequence-specific recognition of DNA by small organic molecules offers a potentially effective approach for the external regulation of gene expression and is an important goal in cell biochemistry. Rational design of compounds from established modules can potentially yield compounds that bind strongly and selectively with specific DNA sequences. An initial approach is to start with common A·T bp recognition molecules and build in G·C recognition units. Here we report on the DNA interaction of a synthetic compound that specifically binds to a G·C bp in the minor groove of DNA by using an azabenzimidazole moiety. The detailed interactions were evaluated with biosensor-surface plasmon resonance (SPR), isothermal calorimetric (ITC), and mass spectrometry (ESI-MS) methods. The compound, DB2277, binds with single G·C bp containing sequences with subnanomolar potency and displays slow dissociation kinetics and high selectivity. A detailed thermodynamic and kinetic study at different experimental salt concentrations and temperatures shows that the binding free energy is salt concentration dependent but essentially temperature independent under our experimental conditions, and binding enthalpy is temperature dependent but salt concentration independent. The results show that in the proper compound structural context novel heterocyclic cations can be designed to strongly recognize complex DNA sequences

Factorizations and Universal Automaton of omega Languages

In this paper, we extend the concept of factorization on finite words to ω-rational languages and show how to compute them. We define a normal form for Büchi automata and introduce a universal automaton for Büchi automata in normal form. We prove that, for every ω-rational language, this Büchi automaton, based on factorization, is canonical and that it is the smallest automaton that contains the morphic image of every equivalent Büchi automaton in normal form