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A Semantic Approach to the Analysis of Rewriting-Based Systems
[article]

2017
*
arXiv
*
pre-print

*rewriting*, non-loopingness

*of*

*conditional*

*rewrite*

*systems*, or the secure access to protected pages

*of*

*a*web site modeled as an order-sorted

*rewrite*theory. ... In this paper we show that

*a*number

*of*interesting properties

*of*

*rewriting*-based

*systems*can be investigated in this way, including infeasibility and non-joinability

*of*critical pairs in (

*conditional*) ... Conclusions and future work We have presented

*a*

*semantic*

*approach*to

*prove*properties

*of*computational

*systems*whose

*semantics*can be given as

*a*Horn theory S. ...

##
###
Termination of String Rewriting Proved Automatically

2005
*
Journal of automated reasoning
*

*of*an extensive class

*of*string

*rewriting*

*systems*(SRSs). ... The tool implementing these techniques is called TORPA:

*Termination*

*of*

*Rewriting*

*Proved*Automatically. ... In particular here we think

*of*liveness problems. • The technique

*of*dependency pairs can be seen as

*a*technique by which

*termination*

*of*

*a*

*rewrite*

*system*is

*proved*via

*proving*relative

*termination*

*of*

*a*...

##
###
Dependency pairs for proving termination properties of conditional term rewriting systems

2017
*
Journal of Logical and Algebraic Methods in Programming
*

This can be used to obtain

doi:10.1016/j.jlamp.2016.03.003
fatcat:hc6ugzjscrhjhlbkdjqzsg656m
*a*powerful and more expressive framework for*proving**termination*properties*of**Conditional*Term*Rewriting**Systems*. ...*semantics**of*the*system*. ...*Termination*, V -*termination*, and operational*termination**of*CTRSs The*semantics**of**rewriting*-based computational*systems*is often described by means*of*the transitions induced by the*rewriting*steps. ...##
###
Proving Termination of Integer Term Rewriting
[chapter]

2009
*
Lecture Notes in Computer Science
*

When using

doi:10.1007/978-3-642-02348-4_3
fatcat:dson7pvncfag5ghgb22ddbxf6u
*rewrite*techniques for*termination*analysis*of*programs,*a*main problem are pre-defined data types like integers. ... We extend term*rewriting*by built-in integers and adapt the dependency pair framework to*prove**termination**of*integer term*rewriting*automatically. ⋆ In Proc. RTA'09, LNCS. ... AProVE08 could only*prove**termination**of*24*of*them (20.5 %) and T T T 2*proved**termination**of*6 examples (5.1 %). This clearly shows the enormous benefits*of*built-in integers in term*rewriting*. ...##
###
Transformational methodology for proving termination of logic programs

1998
*
The Journal of Logic Programming
*

*A*methodology for

*proving*the

*termination*

*of*well-moded logic programs is developed by reducing the

*termination*problem

*of*logic programs to that

*of*term

*rewriting*

*systems*. ...

*A*transformation procedure is presented to derive

*a*term

*rewriting*

*system*from

*a*given well-moded logic program such that the

*termination*

*of*the derived

*rewrite*

*system*implies the

*termination*

*of*the logic ... Klop

*of*CWI for their helpful comments. Thanks are also due to the anonymous referees, whose comments have greatly improved the presentation. Dr. ...

##
###
Proving existential termination of normal logic programs
[chapter]

1996
*
Lecture Notes in Computer Science
*

The followed

doi:10.1007/bfb0014328
fatcat:rble65y7fncptaccx52j64ahuq
*approach*is to develop*a*suitable transformation from logic programs to Term*Rewriting**Systems*(TRSs), such that*proving**termination**of*the obtained TRS implies existential*termination**of*... Moreover, the*approach*i s*a*l s o*a*b l e t o c o p e w i t h t h e dual notion*of*universal*termination*: in fact,*a*whole spectrum*of**termination*properties, said k-*termination*, i s i n vestigated,*of*... from logic programs into TRSs such t h*a*t t o p r o ve the universal*termination**of**a*logic program it su ces to*prove*the*termination**of*the transformed term*rewriting**system*. ...##
###
Matrix Interpretations for Proving Termination of Term Rewriting
[chapter]

2006
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/11814771_47
fatcat:cbdgy345azcnxajxrkhogudnvi
*a*new method for automatically*proving**termination**of*term*rewriting*. ... This method allows to*prove**termination*and relative*termination*. ...*Proving**termination*rather than relative*termination*is*a*special case*of*this*approach*: then S is empty in SN(R/S). to top → R ∪ → S . ...##
###
Matrix Interpretations for Proving Termination of Term Rewriting

2007
*
Journal of automated reasoning
*

We present

doi:10.1007/s10817-007-9087-9
fatcat:rfyy4j545bhg5fjcnrj3btezay
*a*new method for automatically*proving**termination**of*term*rewriting*. ... This method allows to*prove**termination*and relative*termination*. ...*Proving**termination*rather than relative*termination*is*a*special case*of*this*approach*: then S is empty in SN(R/S). to top → R ∪ → S . ...##
###
Proving termination of context-sensitive rewriting by transformation

2006
*
Information and Computation
*

With CSR, we can achieve

doi:10.1016/j.ic.2006.07.001
fatcat:we7uzoolhfa3tpd6jnewlc7wty
*a**terminating*behavior with non-*terminating*term*rewriting**systems*, by pruning (all) infinite*rewrite*sequences. ... Several methods have been developed for*proving**termination**of*CSR. Specifically,*a*number*of*transformations that permit treating this problem as*a*standard*termination*problem have been described. ... This*condition*is based on*proving**termination**of*the so-called -*rewriting**of**a*(*Conditional*) TRS, where -*rewriting*is*rewriting*restricted to top redexes in terms ( [23, Definition 1] ). ...##
###
Proving Termination of Context-Sensitive Rewriting with MU-TERM

2007
*
Electronical Notes in Theoretical Computer Science
*

*Proving*

*termination*

*of*CSR is an interesting problem with several applications in the fields

*of*term

*rewriting*and programming languages. ... Context-sensitive

*rewriting*(CSR) is

*a*restriction

*of*

*rewriting*which forbids reductions on selected arguments

*of*functions. ... In this way, for

*a*given Term

*Rewriting*

*System*(TRS), we obtain

*a*restriction

*of*the

*rewrite*relation which we call context-sensitive

*rewriting*. ...

##
###
A methodology for proving termination of logic programs

1994
*
The Journal of Logic Programming
*

In this paper, we describe

doi:10.1016/0743-1066(94)90004-3
fatcat:5urbmse7pbhuzm7ob3eh7zwrki
*a*methodology for*proving**termination**of*logic programs. ... Such*a*relation enables us to use U-graphs for establishing the universal*termination**of*logic programs. ... Shyamasundar et al. [33] provide*a*characterization*of**termination**of*logic programs through the*termination*characteristics*of*term-*rewriting**systems*. ...##
###
mu-term: A Tool for Proving Termination of Context-Sensitive Rewriting
[chapter]

2004
*
Lecture Notes in Computer Science
*

These orderings can also be used, in

doi:10.1007/978-3-540-25979-4_14
fatcat:v7qxcoyarzgt3a5pzcnjp2g55y
*a*number*of*different ways, for*proving**termination**of*ordinary*rewriting*. ... Restrictions*of**rewriting*can eventually achieve*termination*by pruning all infinite*rewrite*sequences issued from every term. Contextsensitive*rewriting*(CSR) is an example*of*such*a*restriction. ... I thank Albert Rubio and Cristina Borralleras for providing most*of*the proofs (and disproofs)*of**termination**of*CSR with CS-RPO summarized in the aforementioned WWW site. ...##
###
Using Well-Founded Relations for Proving Operational Termination

2019
*
Journal of automated reasoning
*

In this paper, we study operational

doi:10.1007/s10817-019-09514-2
fatcat:mf6q6qghknebhjwawyijyzpaq4
*termination*,*a*proof theoretical notion for capturing the*termination*behavior*of*computational*systems*. ... We*prove*that operational*termination*can be characterized at different levels by means*of*wellfounded relations on specific formulas which can be obtained from the considered*system*. ... , including*Conditional*Term*Rewriting**Systems*(CTRSs) [27, 37, 38] , Membership Equational Theories [8] , and Generalized*Rewriting*Theories [7] , among others (see also [2, 9, 35] ). ...##
###
Methods for Proving Termination of Rewriting-based Programming Languages by Transformation

2009
*
Electronical Notes in Theoretical Computer Science
*

tools for

doi:10.1016/j.entcs.2009.07.062
fatcat:gf3lzx2eb5bl5glrlp7hfz26ia
*proving**termination**of*(variants*of*)*rewriting*. ... The operational meaning*of*such features is often formalized in*a*proof theoretic manner by means*of*an inference*system*rather than just by*a**rewriting*relation. ... (vi) M is*a*set*of**conditional*memberships*of*the form (∀X) t : s if*A*1 ∧ . . . ∧*A*k with the*A*i as before. The inference*system*in Figure 2 defines the execution*semantics**of*SCS-MCTRSs. ...##
###
Polynomials for Proving Termination of Context-Sensitive Rewriting
[chapter]

2004
*
Lecture Notes in Computer Science
*

The latter is the case for context-sensitive

doi:10.1007/978-3-540-24727-2_23
fatcat:dgodjvwoeja3ndv2uqq74wrwvi
*rewriting*(CSR),*a*simple restriction*of**rewriting*which has been*proved*useful for describing the*semantics**of*several programming languages (e.g., Maude) ... For instance, the dependency pairs method for*proving**termination**of**rewriting*, and some restrictions*of*the*rewrite*relation which are not monotonic in all arguments*of*the function symbols, can benefit ... This provides*a*new technique for*proving**termination**of**rewriting*(Example 5) and*a*basis for*proving**termination**of*CSR by means*of*very general polynomial interpretations which can be characterized ...
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