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

Timos Antonopoulos, Nikos Gorogiannis, Christoph Haase, Max Kanovich, Joël Ouaknine
2014 Lecture Notes in Computer Science  
We establish 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.  ... 
doi:10.1007/978-3-642-54830-7_27 fatcat:pxuvp6u335fwzh36fwrsck3ruy

A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic [chapter]

Quang Loc Le, Makoto Tatsuta, Jun Sun, Wei-Ngan Chin
2017 Lecture Notes in Computer Science  
We consider the satisfiability 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  ... 
doi:10.1007/978-3-319-63390-9_26 fatcat:jiyzl6x5hrgohc6jooudtqf33m

SPEN: A Solver for Separation Logic [chapter]

Constantin Enea, Ondřej Lengál, Mihaela Sighireanu, Tomáš Vojnar
2017 Lecture Notes in Computer Science  
SPEN is a solver 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  ... 
doi:10.1007/978-3-319-57288-8_22 fatcat:o27lvwfkaba7hk5yw5h4msjagi

SL-COMP: Competition of Solvers for Separation Logic [chapter]

Mihaela Sighireanu, Juan A. Navarro Pérez, Andrey Rybalchenko, Nikos Gorogiannis, Radu Iosif, Andrew Reynolds, Cristina Serban, Jens Katelaan, Christoph Matheja, Thomas Noll, Florian Zuleger, Wei-Ngan Chin (+12 others)
2019 Msphere  
The first system is a satisfiability solver 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.  ... 
doi:10.1007/978-3-030-17502-3_8 fatcat:nldndal7ofgezlsca4p36shc2u

Suggestions for composing and specifying program design decisions [chapter]

M. Sintzoff
1980 Lecture Notes in Computer Science  
Composition rules based on 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  ... 
doi:10.1007/3-540-09981-6_22 fatcat:w24ynt6z7rcnvea4dagcwsgqcy

Automating Separation Logic Using SMT [chapter]

Ruzica Piskac, Thomas Wies, Damien Zufferey
2013 Lecture Notes in Computer Science  
We show how to use this reduction to automate satisfiability, entailment, frame inference, and abduction 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.  ... 
doi:10.1007/978-3-642-39799-8_54 fatcat:kb6sfaasmrdu5cvfgor4g6jmle

ILP turns 20

Stephen Muggleton, Luc De Raedt, David Poole, Ivan Bratko, Peter Flach, Katsumi Inoue, Ashwin Srinivasan
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  ... 
doi:10.1007/s10994-011-5259-2 fatcat:xetuljrsfzddfogtlj7zse4ura

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.”  ... 

Compositional entailment checking for a fragment of separation logic

Constantin Enea, Ondřej Lengál, Mihaela Sighireanu, Tomáš Vojnar
2017 Formal methods in system design  
We present a (semi-)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).  ... 
doi:10.1007/s10703-017-0289-4 fatcat:ztj4nzmmnffvjhehwgsaof3juu

Compositional Entailment Checking for a Fragment of Separation Logic [chapter]

Constantin Enea, Ondřej Lengál, Mihaela Sighireanu, Tomáš Vojnar
2014 Lecture Notes in Computer Science  
We present a (semi-)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).  ... 
doi:10.1007/978-3-319-12736-1_17 fatcat:nnanvw3ywrefnloiza4bknx6ry

A Decision Procedure for String Logic with Equations, Regular Membership and Length Constraints [article]

Quang Loc Le
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  ... 
arXiv:1610.01331v2 fatcat:fjzftqgztfanhmubp5rgj7g6km

Theorem Proving for Verification [chapter]

John Rushby
2001 Lecture Notes in Computer Science  
The challenges 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  ... 
doi:10.1007/3-540-45510-8_2 fatcat:zkr5qrowengi7pdfitljv6ubv4

Learning the past tense of English verbs using inductive logic programming [chapter]

Raymond J. Mooney, Mary Elaine Califf
1996 Lecture Notes in Computer Science  
It is particularly useful 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 .  ... 
doi:10.1007/3-540-60925-3_60 fatcat:otoxrhk5hbggzntxeqhtm5ebpe

Logic, Probability and Computation: Foundations and Issues of Statistical Relational AI [chapter]

David Poole
2011 Lecture Notes in Computer Science  
I overview the 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  ... 
doi:10.1007/978-3-642-20895-9_1 fatcat:pmfxqtkjafaybore5murr75fra

Inductive logic programming

Stephen Muggleton
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.  ... 
doi:10.1007/bf03037089 fatcat:xdit3d46qfgx5c6frntu4cx3se
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