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On series-parallel pomset languages: Rationality, context-freeness and automata

Tobias Kappé, Paul Brunet, Bas Luttik, Alexandra Silva, Fabio Zanasi
2019 Journal of Logical and Algebraic Methods in Programming  
We also characterise the behavior of general PAs in terms of context-free pomset grammars; consequently, universality, equivalence and series-parallel rationality of general PAs are undecidable.  ...  We show that PAs can implement the BKA semantics of series-parallel rational expressions, and that a class of PAs can be translated back to these expressions.  ...  With all this in hand, we are finally ready to construct series-parallel rational expressions from pomset automata. Lemma 4.8 .  ... 
doi:10.1016/j.jlamp.2018.12.001 fatcat:mkka4j7qwrazlamc6wbaggbqoe

Series-parallel posets: Algebra, automata and languages [chapter]

K. Lodaya, P. Weil
1998 Lecture Notes in Computer Science  
In order to model concurrency, we extend automata theory from the usual word languages (sets of labelled linear orders) to sets of labelled series-parallel posets | or, equivalently, to sets of terms in  ...  an algebra with two product operations: sequential and parallel.  ...  It is easy to express series-parallel languages in this approach, but automata models operating on graphs have proved hard to nd.  ... 
doi:10.1007/bfb0028590 fatcat:76pd54rcvvanldopkvpx54pcii

On Decidability of Concurrent Kleene Algebra

Paul Brunet, Damien Pous, Georg Struth, Marc Herbstritt
2017 International Conference on Concurrency Theory  
Those generated by expressions over the full CKA signature are called series-parallel-rational (spr-languages), those generated by using a signature without the parallel star are called series-rational  ...  Their natural semantics is given by series(-parallel) rational pomset languages, a standard true concurrency semantics, which is often associated with processes of Petri nets.  ...  Lodaya and Weil introduced branching automata that recognise series-parallel rational pomset languages [15] , which include the series-rational languages we use here.  ... 
doi:10.4230/lipics.concur.2017.28 dblp:conf/concur/BrunetPS17 fatcat:m4zsrjlxvjeh3ley44vtudvslu

Concurrent Kleene Algebra: Free Model and Completeness [chapter]

Tobias Kappé, Paul Brunet, Alexandra Silva, Fabio Zanasi
2018 Lecture Notes in Computer Science  
Moreover, the techniques developed along the way are reusable; in particular, they allow us to establish pomset automata as an operational model for CKA.  ...  This result settles a conjecture of Hoare and collaborators.  ...  Our proof of completeness is based on extending an existing completeness result that establishes series-parallel rational pomset languages as the free Bi-Kleene Algebra (BKA) [19] .  ... 
doi:10.1007/978-3-319-89884-1_30 fatcat:f3pehykwszfahjer6t6sn7spmm

Subject index volumes 1–200

1999 Theoretical Computer Science  
of polynomial growth, 197 formal power -, 2242 rational 1, 197 Series-parallel composition, 904 series-parallel graphs, 1661, 3238 transitive vertex -/ 2906 server, 3398 algorithm, 1823 for two  ...  , 1809 cyclic rational -, 1325 of finite image, cyclic rational -, 1325 on regular languages, single-valued rational -, , 1642 time complexity of an algorithm, 3020 recursive real continuous functions  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Subject index volumes 101–150

1995 Theoretical Computer Science  
SO I 213, 302,402,489, 577,603,668.697 recognition 709 control 35, 49, 625, 640, 773 sets 405, 420 automata 625 tree languages 4 IS automata, finite state -625 context-freeness problems  ...  automata 415 exponential ttme SO7 expressions 303 deterministic finite automaton 287. 396, 5.53, see also DFA transducers 231 deterministic gsm 231 language 63 I lower bound 122 one-tape  ... 
doi:10.1016/0304-3975(95)80002-6 fatcat:azbu2orp7vc75pwux4jxnvxl7m

Equational Theories of Scattered and Countable Series-Parallel Posets [chapter]

Amrane Amazigh, Nicolas Bedon
2020 Lecture Notes in Computer Science  
The class SP (A) is built from the letters and closed under the operations of series finite, ω and ω products, and finite parallel product.  ...  In the class ω SP (A), ω and ω products are replaced by ω and ω powers.  ...  One of them pointed out that Theorem 3 can be deduced from Theorem 1 using the theory of categories, and in particular works by Fiore and Hur [13] , Robinson [19] , Adámek, Rosicky, Velbil et al.  ... 
doi:10.1007/978-3-030-48516-0_1 fatcat:dtuhf4lzg5dzbdaylbpas2i6t4