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Characterizing Languages by Normalization and Termination in String Rewriting [chapter]

Jeroen Ketema, Jakob Grue Simonsen
2012 Lecture Notes in Computer Science  
We characterize sets of strings using two central properties from rewriting: normalization and termination.  ...  " alphabet (and extend the result to termination).  ...  Conclusion and future work We have considered the problem of characterizing sets of strings as the sets of normalizing, resp. terminating, strings over a finite string rewriting system.  ... 
doi:10.1007/978-3-642-31653-1_41 fatcat:c6ijtd4me5g7vflu7zygyiifq4

Structured Production System (extended abstract) [article]

Yi Zhou
2017 arXiv   pre-print
In this extended abstract, we propose Structured Production Systems (SPS), which extend traditional production systems with well-formed syntactic structures.  ...  Also, many fundamental approaches in computer science, including automata, grammar and logic, can be captured by structured production systems.  ...  Abstract rewriting systems and state transition systems Abstract rewriting systems and state transition systems are simple models for modeling dynamics.Similar to automaton, an abstract rewriting system  ... 
arXiv:1704.07950v1 fatcat:ne2grjwllndttoo33fisoloh7i

Non-commutative computation, depth reduction, and skew circuits (extended abstract) [chapter]

Meena Mahajan, V Vinay
1994 Lecture Notes in Computer Science  
I am sincerely thankful to her for spending time for discussions with me, constantly motivating me and developing an enthusiasm in me to work and for being patient with me.  ...  Context-free languages recognition problem is complete for LogCFL. Given: Chomsky Normal form grammar G for language L and a string w = a 1 a 2 ...a n a string to be recognized. Problem: Is w ∈ L?  ...  NP characterized as Programs over Groupoids and its restrictions In (Muscholl, 1992) , it was established that a language is in NP if and only if it is recognized by uniform programs over exponential-order  ... 
doi:10.1007/3-540-58715-2_113 fatcat:xyoamfty75aozjmlbwewnx7dgi

On the representation of infinite temporal data and queries (extended abstract)

Marianne Baudinet, Marc Niézette, Pierre Wolper
1991 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '91  
-language L is nitely regular if there is a regular language L 0 such that L can be obtained from L 0 by extending all the words of L 0 to in nite strings in all possible ways.  ...  Generalized Programs We adopt a normalized form for extensional databases and we rewrite our deductive programs so that deductive rules can operate directly on generalized tuples.  ... 
doi:10.1145/113413.113439 dblp:conf/pods/BaudinetNW91 fatcat:ket5al6vtjg63m3gwm62agkpiu

Page 5885 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
Summary: “This paper extends the termination proof techniques based on rewrite orderings to a higher-order setting, by defining a recursive path ordering for simply typed higher-order terms in n-long B-normal  ...  In particular, it is shown that it is undecidable in general whether a finite, length- reducing, and confluent string-rewriting system yields a regular set of normal forms for each regular language.”  ... 

Proving non-termination by finite automata

Jörg Endrullis, Hans Zantema, Marc Herbstritt
2015 International Conference on Rewriting Techniques and Applications  
It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula.  ...  The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms.  ...  For a string automaton (= NFA) S define the tree automaton A by taking the same sets of states and accepting states, and taking as signature the same signature in which all symbols are unary, extended  ... 
doi:10.4230/lipics.rta.2015.160 dblp:conf/rta/EndrullisZ15 fatcat:kzsyar7vkfer7hqai5qcq24gdi

Representing Languages by Learnable Rewriting Systems [chapter]

Rémi Eyraud, Colin de la Higuera, Jean-Christophe Janodet
2004 Lecture Notes in Computer Science  
Powerful methods and algorithms are known to learn regular languages. Aiming at extending them to more complex grammars, we choose to change the way we represent these languages.  ...  Moreover, SRS constitute an efficient (often linear) parsing device for strings, and are thus promising and challenging candidates in forthcoming applications of Grammatical Inference.  ...  More precisely, the Dyck language is completely characterized by this single rewrite rule and the string λ, which is reached by rewriting all other strings of the language.  ... 
doi:10.1007/978-3-540-30195-0_13 fatcat:tssc3vscvzb6rab22gf4ypfscm

Page 571 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
These abstract struc- tures are used for studying general properties of rewriting systems.  ...  The paper closes with a detailed analysis of two reduction graphs, which are generated in a constructive way by certain simple graph- rewriting rules.  ... 

Rewriting P Systems with Conditional Communication [chapter]

Paolo Bottoni, Anna Labella, Carlos Martín-Vide, Gheorghe PĂun
2002 Lecture Notes in Computer Science  
In this paper we consider systems with string-objects processed by rewriting, with the communication controlled by conditions on the contents of the strings.  ...  Many of the obtained variants lead to new characterizations of recursively enumerable languages (as expected, these characterizations indicate a trade-off between the number of membranes and the strength  ...  Rewriting steps in these normal forms are simulated by coordinating the sequential use of context-free rules.  ... 
doi:10.1007/3-540-45711-9_18 fatcat:frd26hjglrf75fekwhju5g6bry

Proving Looping and Non-Looping Non-Termination by Finite Automata [article]

Jörg Endrullis, Hans Zantema
2015 arXiv   pre-print
The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms.  ...  It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula.  ...  In [24] it has been shown that this monotonicity property is strong enough to characterize and decide the closure of the regular languages under rewriting.  ... 
arXiv:1505.00478v1 fatcat:wknmoo7a6zeubi64dn6yoai6gm

Page 647 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
In an extended simple eco- grammar system we distinguish a subset of the alphabet of the system and only strings over this subalphabet are in the generated language.  ...  This result is closely related to a similar characterization found by Engelfriet and Heyker for the case of string graphs.  ... 

Natural Transformations as Rewrite Rules and Monad Composition [article]

Dexter Kozen
2018 arXiv   pre-print
We show that a given tuple (T,μ,η) is a monad if and only if T is a terminal object in a certain category of strings and rewrite rules, and that this fact can be established by proving confluence of the  ...  We also give a characterization of adjunctions in terms of rewrite categories.  ...  In the presence of η, T is no longer a normal form, and in fact normal forms in the strict sense of string rewriting no longer exist. Nevertheless, T is still a terminal object.  ... 
arXiv:1612.07273v2 fatcat:n462so4gfrhnpowarxouhsskga

Match-Bounded String Rewriting Systems

Alfons Geser, Dieter Hofbauer, Johannes Waldmann
2004 Applicable Algebra in Engineering, Communication and Computing  
We introduce a new class of automated proof methods for the termination of rewriting systems on strings. The basis of all these methods is to show that rewriting preserves regular languages.  ...  Using recent results on deleting systems, we prove that rewriting by a match-bounded system preserves regular languages.  ...  This research was supported in part by the National Aeronautics and Space Administration (NASA) while the last two authors were visiting scientists at the Institute for Computer Applications in Science  ... 
doi:10.1007/s00200-004-0162-8 fatcat:eshe4tyfqrhgrhkgx7k4xjtfvy

Match-Bounded String Rewriting Systems [chapter]

Alfons Geser, Dieter Hofbauer, Johannes Waldmann
2003 Lecture Notes in Computer Science  
We introduce a new class of automated proof methods for the termination of rewriting systems on strings. The basis of all these methods is to show that rewriting preserves regular languages.  ...  Using recent results on deleting systems, we prove that rewriting by a match-bounded system preserves regular languages.  ...  This research was supported in part by the National Aeronautics and Space Administration (NASA) while the last two authors were visiting scientists at the Institute for Computer Applications in Science  ... 
doi:10.1007/978-3-540-45138-9_39 fatcat:lh6d32nalrdf5h7mi443qxstyi

Code generation by model transformation: a case study in transformation modularity

Zef Hemel, Lennart C. L. Kats, Danny M. Groenewegen, Eelco Visser
2009 Journal of Software and Systems Modeling  
Instead of coarse-grained stages that alternate between normalization and type analysis, we have developed a new style of type analysis that can be integrated with normalizing transformations in a fine-grained  ...  The normalization strategy has a simple extension interface and integrates non-local, context-sensitive transformation rules.  ...  This research was supported by NWO/JACQUARD project 638.001.610, MoDSE: Model-Driven Software Evolution, and 612.063.512, TFA: Transformations for Abstractions.  ... 
doi:10.1007/s10270-009-0136-1 fatcat:pyapirp4rfh3tcr3iwli7pfufe
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