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Context-Free Commutative Grammars with Integer Counters and Resets [article]

Dmitry Chistikov, Christoph Haase, Simon Halfon
2016 arXiv   pre-print
We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them.  ...  Those grammars can alternatively be viewed as an extension of communication-free Petri nets. Our main results are that reachability and coverability are inter-reducible and both NP-complete.  ...  We would like to thank Sylvain Schmitz, Philippe Schnoebelen and the anonymous reviewers of RP'14 for their helpful comments and suggestions on an earlier version of this paper.  ... 
arXiv:1511.04893v2 fatcat:s4oz5hconbextbxx5urudqzraa

Context-free commutative grammars with integer counters and resets

Dmitry Chistikov, Christoph Haase, Simon Halfon
2018 Theoretical Computer Science  
We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them.  ...  Those grammars can alternatively be viewed as an extension of communication-free Petri nets. Our main results are that reachability and coverability are inter-reducible and both NPcomplete.  ...  We would like to thank Sylvain Schmitz, Philippe Schnoebelen and the anonymous reviewers of RP'14 for their helpful comments and suggestions on an earlier version of this paper.  ... 
doi:10.1016/j.tcs.2016.06.017 fatcat:kkcyianwrzbghkcbrfmofxl2mu

Integer Vector Addition Systems with States [chapter]

Christoph Haase, Simon Halfon
2014 Lecture Notes in Computer Science  
A ZVASS comprises a finite-state controller with a finite number of counters ranging over the integers.  ...  This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof.  ...  We would like to thank the anonymous referees, Sylvain Schmitz and Philippe Schnoebelen for their helpful comments and suggestions on an earlier version of this paper.  ... 
doi:10.1007/978-3-319-11439-2_9 fatcat:7pvckuxbvzfrvkecxg2wqrkaum

Extended Models of Finite Automata [article]

Özlem Salehi
2019 arXiv   pre-print
We establish a link between the decision problems of matrix semigroups and the corresponding automata. We present some new results about valence pushdown automata and context-free valence grammars.  ...  We investigate the language recognition power of finite automata over integer and rational matrix groups and reveal new relationships between the language classes corresponding to these models.  ...  [8] Context-free valence grammars over finite or commutative monoids are not stronger than context-free valence grammars over finite or commutative groups.  ... 
arXiv:1912.11699v1 fatcat:umb4afgbhzatratlrleuvnrmmm

Timed Pushdown Automata Revisited

Lorenzo Clemente, Slawomir Lasota
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
Motivated by this result, we advocate the framework of firstorder definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA.  ...  As our first result we prove that the model of dense-timed PDA of Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with timeless stack.  ...  Timed register context-free grammars Context-free grammars are PDA with one state where each transition pops exactly one symbol off the stack.  ... 
doi:10.1109/lics.2015.73 dblp:conf/lics/ClementeL15 fatcat:ouvyt74aefaopf2cv2t2gzan74

Timed pushdown automata revisited [article]

Lorenzo Clemente, Sławomir Lasota
2015 arXiv   pre-print
Motivated by this result, we advocate the framework of first-order definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA.  ...  As our first result we prove that the model of dense-timed PDA of Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with timeless stack.  ...  Timed register context-free grammars Context-free grammars are PDA with one state where each transition pops exactly one symbol off the stack.  ... 
arXiv:1503.02422v2 fatcat:bb4ty4pbobfx3auogilc5rlevy

On the intersection of stacks and queues

Franz J. Brandenburg
1988 Theoretical Computer Science  
by machines with a pushdown, a queue and a counter, and their one-reversal restrictions respectively. 0304.3975/88/$3.50  ...  In fact, there is a complete lattice of new families of languages between the regular languages and the context-free languages, obtained by the intersection of the families of languages that are defined  ...  They can be obtained from the characterization of the linear context-free languages by linear context-free grammars, and dually, of the single-reset languages by equal matrix grammars.  ... 
doi:10.1016/0304-3975(88)90019-9 fatcat:u4vs2pskuneble7fxhvjhwxo5a

Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages [chapter]

Tero Harju, Oscar Ibarra, Juhani Karhumäki, Arto Salomaa
2001 Lecture Notes in Computer Science  
We also prove a surprising undecidability result for commutation of languages: given a fixed two element code Ã, it is undecidable whether a given context-free language Ä commutes with Ã, i.e., ÄÃ ÃÄ.  ...  Let be a class of automata (in a precise sense to be defined) and be the class obtained by augmenting each automaton in with finitely many reversal-bounded counters.  ...  The classical result in [P66] states that the commutative image of a context-free language is semilinear, and that it can be effectively constructed from the pushdown automaton (or the context-free grammar  ... 
doi:10.1007/3-540-48224-5_48 fatcat:gvlbyixy75exfj72xib7zzybly

Some Decision Problems Concerning Semilinearity and Commutation

Tero Harju, Oscar Ibarra, Juhani Karhumäki, Arto Salomaa
2002 Journal of computer and system sciences (Print)  
We also prove a surprising undecidability result for commutation of languages: given a fixed two-element code K, it is undecidable whether a given context-free language L commutes with K, i.e., LK ¼ KL  ...  Let M be a class of automata (in a precise sense to be defined) and M c the class obtained by augmenting each automaton in M with finitely many reversal-bounded counters.  ...  The classical result in [18] states that the commutative image of a context-free language is semilinear, and that it can be effectively constructed from the pushdown automaton (or the context-free grammar  ... 
doi:10.1006/jcss.2002.1836 fatcat:jbmvukk7o5d67dhmzhza3u47gi

Nivat's theorem for pushdown transducers

Georg Karner
1992 Theoretical Computer Science  
The equivalence to "nonextended" PDAs and PDTs is shown. The semiring structure gives a new proof that the types reset-pushdown and one-counter are real-time types.  ...  As an important application, Nivat's theorem is generalized to rational and polynomial PDTs over arbitrary semirings. Examples include the mirror image of the input and the Dyck reduction.  ...  Kuich for initiating the research and for many helpful discussions.  ... 
doi:10.1016/0304-3975(92)90077-s fatcat:bdiscvbb65aqxcjncpwany3nvm

Revisiting Reachability in Timed Automata [article]

Karin Quaas, Mahsa Shirmohammadi, James Worrell
2017 arXiv   pre-print
and reals.  ...  We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers  ...  This work was partially supported by the EPSRC through grants EP/M012298/1 and EP/M003795/1 and by the German Research Foundation (DFG), project QU 316/1-2.  ... 
arXiv:1702.03450v2 fatcat:jfqgafejabebzkz53uqueq5e4a

Automatic Verification of Multi-queue Discrete Timed Automata [chapter]

Pierluigi San Pietro, Zhe Dang
2003 Lecture Notes in Computer Science  
The MQDTA model can be used to specify and verify various systems with unbounded queues, such as a real-time scheduler.  ...  We propose a new infinite-state model, called the Multi-queue Discrete Timed Automaton MQDTA, which extends Timed Automata with queues, but only has integer-valued clocks.  ...  Here, we consider the Generalized Context-free Grammars ( ¢ ¡ £ ) of [8] , which use both queues and stacks with suitable constraints to generate only semilinear languages, and which are well suited  ... 
doi:10.1007/3-540-45071-8_18 fatcat:dktetd4myvfotf4dzhruo7vhaq

QRT FIFO automata, breadth-first grammars and their relations

Alessandra Cherubini, Claudio Citrini, Stefano Crespi Reghizzi, Dino Mandrioli
1991 Theoretical Computer Science  
Reghizzi, and D. Mandrioli, QRT FIFO automata, breadth-first grammars and their relations, Theoretical Computer Science 85 (1991) 171-203.  ...  Brandenburg for helpful comments on a previous draft and for indicating some useful references.  ...  In Section 5 we consider breadth-first context-free grammars and recall their basic properties.  ... 
doi:10.1016/0304-3975(91)90053-5 fatcat:6s23j5uqezdbzj5bd3iottq6me

Bounded underapproximations

Pierre Ganty, Rupak Majumdar, Benjamin Monmege
2012 Formal methods in system design  
We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L' included in L which has the same Parikh (  ...  counter programs.  ...  We thank Javier Esparza for his help on the lower bounds on the bounded expressions which solves Pb. 1 for regular and context-free languages given at Lemma 8 and 13, respectively.  ... 
doi:10.1007/s10703-011-0136-y fatcat:joo3r6istjau7g7c4u6hhbxkha

Bounded Underapproximations [chapter]

Pierre Ganty, Rupak Majumdar, Benjamin Monmege
2010 Lecture Notes in Computer Science  
We show a new and constructive proof of the following languagetheoretic result: for every context-free language L, there is a bounded context-free language L ⊆ L which has the same Parikh (commutative)  ...  Bounded languages, introduced by Ginsburg and Spanier, are subsets of regular languages of the form  ...  We thank Javier Esparza for his help on the lower bounds on the bounded expressions which solves Pb. 1 for regular and context-free languages given at Lemma 8 and 13, respectively.  ... 
doi:10.1007/978-3-642-14295-6_52 fatcat:zqrqymahgnccfjudn4h3ofzzza
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