Commutative Languages and their Composition by Consensual Methods

Commutative languages with the semilinear property (SLIP) can be naturally recognized by real-time NLOG-SPACE multi-counter machines. We show that unions and concatenations of such languages can be similarly recognized, relying on -- and further developing, our recent results on the family of consensually regular (CREG) languages. A CREG language is defined by a regular language on the alphabet that includes the terminal alphabet and its marked copy. New conditions, for ensuring that the union or concatenation of CREG languages is closed, are presented and applied to the commutative SLIP languages. The paper contributes to the knowledge of the CREG family, and introduces novel techniques for language composition, based on arithmetic congruences that act as language signatures. Open problems are listed.Comment: In Proceedings AFL 2014, arXiv:1405.527

Dense-choice Counter Machines revisited

This paper clarifies the picture about Dense-choice Counter Machines, which have been less studied than (discrete) Counter Machines. We revisit the definition of "Dense Counter Machines" so that it now extends (discrete) Counter Machines, and we provide new undecidability and decidability results. Using the first-order additive mixed theory of reals and integers, we give a logical characterization of the sets of configurations reachable by reversal-bounded Dense-choice Counter Machines

Deciding the Satisfiability of MITL Specifications

In this paper we present a satisfiability-preserving reduction from MITL interpreted over finitely-variable continuous behaviors to Constraint LTL over clocks, a variant of CLTL that is decidable, and for which an SMT-based bounded satisfiability checker is available. The result is a new complete and effective decision procedure for MITL. Although decision procedures for MITL already exist, the automata-based techniques they employ appear to be very difficult to realize in practice, and, to the best of our knowledge, no implementation currently exists for them. A prototype tool for MITL based on the encoding presented here has, instead, been implemented and is publicly available.Comment: In Proceedings GandALF 2013, arXiv:1307.416

from regular to strictly locally testable languages

Comment: In Proceedings WORDS 2011, arXiv:1108.341

From words to pictures: Row-column combinations and Chomsky-Schützenberger theorem

The row-column combination RCC maps two (word) languages over the same alphabet onto the set of rectangular arrays, i.e., pictures, such that each row/column is a word of the first/second language. The resulting array is thus a crossword of the component words. Depending on the family of the components, different picture (2D) language families are obtained: e.g., the well-known tiling-system recognizable languages are the alphabetic projection of the crossword of local (regular) languages. We investigate the effect of the RCC operation especially when the components are context-free, also with application of an alphabetic projection. The resulting 2D families are compared with others defined in the past. The classical characterization of context-free languages, known as Chomsky-Schützenberger theorem, is extended to the crosswords in this way: the projection of a context-free crossword is equivalent to the projection of the intersection of a 2D Dyck language and the crossword of strictly locally testable language. The definition of 2D Dyck language relies on a new more flexible so-called Cartesian RCC operation on Dyck languages. The proof involves the version of the Chomsky-Schützenberger theorem that is non-erasing and uses a grammar-independent alphabet

Bounded Reachability for Temporal Logic over Constraint Systems

We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such logic can be undecidable. We introduce suitable restrictions and assumptions that are shown to make the satisfiability problem for the extended logic decidable. Moreover for a large class of constraint systems we propose an encoding that realize an effective decision procedure for the Bounded Reachability problem