16 research outputs found
Star-Free Languages are Church-Rosser Congruential
The class of Church-Rosser congruential languages has been introduced by
McNaughton, Narendran, and Otto in 1988. A language L is Church-Rosser
congruential (belongs to CRCL), if there is a finite, confluent, and
length-reducing semi-Thue system S such that L is a finite union of congruence
classes modulo S. To date, it is still open whether every regular language is
in CRCL. In this paper, we show that every star-free language is in CRCL. In
fact, we prove a stronger statement: For every star-free language L there
exists a finite, confluent, and subword-reducing semi-Thue system S such that
the total number of congruence classes modulo S is finite and such that L is a
union of congruence classes modulo S. The construction turns out to be
effective
Omega-rational expressions with bounded synchronization delay
© 2013, Springer Science+Business Media New York. In 1965 Sch ̈utzenberger published his famous result that star-free
languages (SF) and aperiodic languages (AP) coincide over finite words, often
written as SF = AP. Perrin generalized SF = AP to infinite words in the mid
1980s. In 1973 Sch ̈utzenberger presented another (and less known) characteri-
zation of aperiodic languages in terms of rational expressions where the use of
the star operation is restricted to prefix codes with bounded synchronization
delay and no complementation is used. We denote this class of languages by
SD. In this paper, we present a generalization of SD = AP to infinite words.
This became possible via a substantial simplification of the proof for the cor-
responding result for finite words. Moreover, we show that SD = AP can be
viewed as more fundamental than SF = AP in the sense that the classical 1965
result of Sch ̈utzenberger and its 1980s extension to infinite words by Perrin
are immediate consequences of SD = AP
Truly Concurrent Logic via In-Between Specification
AbstractIn order to obtain a formalism for the specification of true concurrency in reactive systems, we modify the μ-calculus such that properties that are valid during the execution of an action can be expressed. The interpretation of this logic is based on transition systems that are used to model the ST-semantics. We show that this logic and step equivalence have an incomparable expressive power. Furthermore, we show that the logic characterizes the ST-bisimulation equivalence for finite process algebra expressions that do not contain synchronization mechanisms
A Survey on the Local Divisor Technique
Local divisors allow a powerful induction scheme on the size of a monoid. We
survey this technique by giving several examples of this proof method. These
applications include linear temporal logic, rational expressions with Kleene
stars restricted to prefix codes with bounded synchronization delay,
Church-Rosser congruential languages, and Simon's Factorization Forest Theorem.
We also introduce the notion of localizable language class as a new abstract
concept which unifies some of the proofs for the results above
Pure future local temporal logics are expressively complete for Mazurkiewicz traces
AbstractThe paper settles a long standing problem for Mazurkiewicz traces: the pure future local temporal logic defined with the basic modalities exists-next and until is expressively complete. This means every first-order definable language of Mazurkiewicz traces can be defined in a pure future local temporal logic. The analogous result with a global interpretation has been known, but the treatment of a local interpretation turned out to be much more involved. Local logics are interesting because both the satisfiability problem and the model checking problem are solvable in Pspace for these logics whereas they are non-elementary for global logics. Both, the (previously known) global and the (new) local results generalize Kamp’s Theorem for words, because for sequences local and global viewpoints coincide