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Foundations for Decision Problems in Separation Logic with General Inductive Predicates
[chapter]

2014
*
Lecture Notes in Computer Science
*

We establish

doi:10.1007/978-3-642-54830-7_27
fatcat:pxuvp6u335fwzh36fwrsck3ruy
*foundational*results on the computational complexity of deciding entailment*in**Separation**Logic**with**general**inductive**predicates*whose underlying base language allows*for*pure formulas, pointers ... We additionally show that entailment*in*essentially any fragment of*Separation**Logic*allowing*for**general**inductive**predicates*is intractable even when strong syntactic restrictions are imposed. * Supported ...*In*particular, we wish to thank one referee who suggested the reduction from the inclusion*problem**for*tree automata*for*the proof of Theorem 5. ...##
###
A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic
[chapter]

2017
*
Lecture Notes in Computer Science
*

We consider the satisfiability

doi:10.1007/978-3-319-63390-9_26
fatcat:jiyzl6x5hrgohc6jooudtqf33m
*problem**for*a fragment of*separation**logic*including*inductive**predicates**with*shape and arithmetic properties. ... Our*decision*procedure is based on a novel algorithm to infer a finite representation*for*each*inductive**predicate*which precisely characterises its satisfiability. ... A*decision*procedure*for*satisfiability of*separation**logic**with**inductive**predicates*could be useful*for*multiple analysis*problems*associated*with*heapmanipulating programs, e.g., compositional verification ...##
###
SPEN: A Solver for Separation Logic
[chapter]

2017
*
Lecture Notes in Computer Science
*

SPEN is a solver

doi:10.1007/978-3-319-57288-8_22
fatcat:o27lvwfkaba7hk5yw5h4msjagi
*for*a fragment of*separation**logic*(SL)*with**inductively*-defined*predicates*covering both (nested) list structures as well as various kinds of trees, possibly extended*with*data. ... The solver has been successfully applied to a rather large benchmark of various*problems*issued from program verification tools. ...*Logic*Fragment SPEN deals*with**decision**problems**in*a fragment of SL, denoted as SL ID , that combines the symbolic heaps fragment of SL [1]*with*user-defined*inductive**predicates*describing various ...##
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SL-COMP: Competition of Solvers for Separation Logic
[chapter]

2019
*
Msphere
*

The first system is a satisfiability solver

doi:10.1007/978-3-030-17502-3_8
fatcat:nldndal7ofgezlsca4p36shc2u
*in**separation**logic**with**general**inductive**predicates*and arithmetic (fragment SLIDLIA). ... It is an instantiation of the theorem prover Cyclist-SL*for*the case of*Separation**Logic**with**inductive*definitions. ...##
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Suggestions for composing and specifying program design decisions
[chapter]

1980
*
Lecture Notes in Computer Science
*

Composition rules based on

doi:10.1007/3-540-09981-6_22
fatcat:w24ynt6z7rcnvea4dagcwsgqcy
*logic*are given*for*these hierarchical specifications. Advantages and disadvantages of the suggestions are assessed (~) Philips Research Lab., av. ... It is proposed to express program designs by hierarchical specifications of design*decisions*. A case study of program construction is presented to substantiate the proposal. ...*For*instance, instead of obtaining the complete*predicate*H by*induction*on the structure of the*predicates*J,J'*in*Dec 33, we could derive Dec 4 by*induction*on ~he dexTsion Dec 32 itself ; as a by-product ...##
###
Automating Separation Logic Using SMT
[chapter]

2013
*
Lecture Notes in Computer Science
*

We show how to use this reduction to automate satisfiability, entailment, frame inference, and abduction

doi:10.1007/978-3-642-39799-8_54
fatcat:kb6sfaasmrdu5cvfgor4g6jmle
*problems**for**separation**logic*using SMT solvers. ... However, these provers cannot be easily extended or combined*with*solvers*for*other theories that are important*in*program verification, e.g., linear arithmetic. ... Conclusions We presented a reduction of decidable*separation**logic*fragments to a decidable firstorder*logic*fragment called GRASS. ...##
###
ILP turns 20

2011
*
Machine Learning
*

*Inductive*

*Logic*Programming (ILP) is an area of Machine Learning which has now reached its twentieth year. ... We show how

*in*each phase ILP has been characterised by an attempt to extend theory and implementations

*in*tandem

*with*the development of novel and challenging real-world applications. ... SM also acknowledges the support of Syngenta Ltd

*in*the University Innovation Centre at Imperial College and the BBSRC

*for*their funding of the Centre

*for*Integrative Systems Biology at Imperial College ...

##
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Page 4019 of Mathematical Reviews Vol. 58, Issue 6
[page]

1979
*
Mathematical Reviews
*

*Logic*and

*Foundations*58 #27201 02 A model of a formal theory consists of a universe of. individuals

*with*distinguished

*predicates*and operations. ... Finally, we conclude

*with*an indi- cation of important

*problems*remaining to be solved and

*with*a few

*general*morals about the study of Wittgenstein’s writings.” ...

##
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Compositional entailment checking for a fragment of separation logic

2017
*
Formal methods in system design
*

We present a (semi-)

doi:10.1007/s10703-017-0289-4
fatcat:ztj4nzmmnffvjhehwgsaof3juu
*decision*procedure*for*checking entailment between*separation**logic*formulas*with**inductive**predicates*specifying complex data structures corresponding to finite nesting of various ... The*decision*procedure is compositional*in*the sense that it reduces the*problem*of checking entailment between two arbitrary formulas to the*problem*of checking entailment between a formula and an atom ... Implementation and Experimental Results We implemented our*decision*procedure*in*a solver called SPEN (*SeParation**logic*ENtailment). ...##
###
Compositional Entailment Checking for a Fragment of Separation Logic
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present a (semi-)

doi:10.1007/978-3-319-12736-1_17
fatcat:nnanvw3ywrefnloiza4bknx6ry
*decision*procedure*for*checking entailment between*separation**logic*formulas*with**inductive**predicates*specifying complex data structures corresponding to finite nesting of various ... The*decision*procedure is compositional*in*the sense that it reduces the*problem*of checking entailment between two arbitrary formulas to the*problem*of checking entailment between a formula and an atom ... Implementation and Experimental Results We implemented our*decision*procedure*in*a solver called SPEN (*SeParation**logic*ENtailment). ...##
###
A Decision Procedure for String Logic with Equations, Regular Membership and Length Constraints
[article]

2016
*
arXiv
*
pre-print

*In*this paper, we consider the satisfiability

*problem*

*for*string

*logic*

*with*equations, regular membership and Presburger constraints over length functions. ...

*In*particular, we propose a semi-

*decision*procedure

*for*arbitrary string formulae

*with*word equations, regular membership and length functions. ... As the S2SAT framework naturally supports arbitrary user-defined

*predicates*, we might extend the proposed

*decision*procedure

*with*

*inductive*

*predicates*encoding recursive string functions (i.e., function ...

##
###
Theorem Proving for Verification
[chapter]

2001
*
Lecture Notes in Computer Science
*

The challenges

doi:10.1007/3-540-45510-8_2
fatcat:zkr5qrowengi7pdfitljv6ubv4
*in*using theorem proving*for*verification of parallel systems are to achieve adequate automation, and to allow human guidance to be expressed*in*terms of the system under examination rather ...*generally*eschew them. 3 Unquantified*logics*such as ACL2 avoid the*problem*of instantiation, but instead must use*induction*(arguably a harder*problem*)*in*similar situations. ... A.1*Inductive*Invariance Proof We begin by specifying what it means*for**predicate*INV to be an*inductive*invariant of a transition relation R*with*initiality*predicate*INIT, and then establish as our first ...##
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Learning the past tense of English verbs using inductive logic programming
[chapter]

1996
*
Lecture Notes in Computer Science
*

It is particularly useful

doi:10.1007/3-540-60925-3_60
fatcat:otoxrhk5hbggzntxeqhtm5ebpe
*for**problems*that involve rules*with*speci c exceptions, such as the past-tense task. ... This paper presents results on using a new*inductive**logic*programming method called Foidl to learn the past tense of English verbs. ... A fuller discussion of this research appears*in*13 . ...##
###
Logic, Probability and Computation: Foundations and Issues of Statistical Relational AI
[chapter]

2011
*
Lecture Notes in Computer Science
*

I overview the

doi:10.1007/978-3-642-20895-9_1
fatcat:pmfxqtkjafaybore5murr75fra
*foundations*of the area, give some research*problems*, proposed solutions, outstanding issues, and clear up some misconceptions that have arisen. ... Over the last 25 years there has been considerable body of research into combinations of*predicate**logic*and probability forming what has become known as (perhaps misleadingly) statistical relational artificial ... Learning from such datasets has been studied under the umbrella of*inductive**logic*programming (ILP) [12, 10] mainly because*logic*programs provide a good representation*for*the*generalizations*required ...##
###
Inductive logic programming

1991
*
New generation computing
*

*In*terms of

*logic*we provide a unifying framework

*for*Muggleton and Buntine's Inverse Resolution (IR) and Plotkin's Relative Least

*General*Generalisation (RLGG) by rederiving RLGG

*in*terms of IR. ... A new research area,

*Inductive*

*Logic*Programming, is presently emerging. ... The author would like to thank Wray Buntine, Cao Feng, Michael Bain and Donald Michie

*for*their helpful discussions and advice. ...

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