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Memory-Efficient Fixpoint Computation [article]

Sung Kook Kim, Arnaud J. Venet, Aditya V. Thakur
2020 arXiv   pre-print
Computationally, abstract interpretation reduces the problem of inferring program invariants to computing a fixpoint of a set of equations.  ...  This paper presents a method to minimize the memory footprint in Bourdoncle's iteration strategy, a widely-used technique for fixpoint computation.  ...  For improving space efficiency, their approach recomputes values during fixpoint computation, and does not prove optimality, unlike our approach.  ... 
arXiv:2009.05865v1 fatcat:kfvoghslszhrxau2kgagwjmn7u

Efficient fixpoint computation in linear tabling

Neng-Fa Zhou, Taisuke Sato
2003 Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming - PPDP '03  
The idea of linear tabling is to use iterative computation rather than suspension to compute fixpoints.  ...  Early resolution mechanisms proposed for tabling such as OLDT rely on suspension and resumption of subgoals to compute fixpoints.  ...  Blind re-computation of all subgoals and clauses is not computationally acceptable.  ... 
doi:10.1145/888251.888277 dblp:conf/ppdp/ZhouS03 fatcat:b53f3ggrtff2zh4dedy7l4wfce

Propagating differences: An efficient new fixpoint algorithm for distributive constraint systems [chapter]

Christian Fecht, Helmut Seidl
1998 Lecture Notes in Computer Science  
Especially, this least solution is monotonic. u t 6 Local Fixpoint Computation Assume set V of variables is tremendously large while at the same time we are only interested in the values for a rather small  ...  As far we know, an application independent exposition for worklist based solvers has not considered before. 9 The Di erential Fixpoint Algorithm Assume variable y has changed its value.  ... 
doi:10.1007/bfb0053565 fatcat:3erobddvzrcvpgml3yzxcaiexm

An Efficient, Parametric Fixpoint Algorithm for Analysis of Java Bytecode

Mario Méndez, Jorge Navas, Manuel V. Hermenegildo
2007 Electronical Notes in Theoretical Computer Science  
We argue that the design of an efficient fixpoint algorithm is pivotal to support the analysis of large programs.  ...  However, while most of the existing work deals with the problem of finding expressive abstract domains that track accurately the characteristics of a particular concrete property, the underlying fixpoint  ...  Thus, we need to mark it as fixpoint and start its fixpoint computation again. Finally, after a fixpoint computation is reached we need to verify the Ids contained in the set of Ids.  ... 
doi:10.1016/j.entcs.2007.02.060 fatcat:z46vc4jhmjcjje2jggj2vdwzgy

Local Model Checking Algorithm Based on Mu-calculus with Partial Orders

Hua Jiang, Qianli Li, Rongde Lin
2017 TELKOMNIKA (Telecommunication Computing Electronics and Control)  
This paper analyzes the computing process of alternating fixpoint nested in detail and designs an efficient local model checking algorithm based on the propositional μ-calculus by a group of partial ordered  ...  It is more efficient than algorithms of previous research. fixpoint theory and designed a global algorithm, the time complexity of the global algorithm was /2 1 ((2 1) ) d On   , and the space complexity  ...  The nested bound algorithm reduces repetitive computation and improves the computational efficiency.  ... 
doi:10.12928/telkomnika.v15i1.3546 fatcat:ghjgiq63rjejblqy5djg7n2qwa

Efficient Decision Procedures for Model Checking of Linear Time Logic Properties [chapter]

Roderick Bloem, Kavita Ravi, Fabio Somenzi
1999 Lecture Notes in Computer Science  
Each fixpoint is thus translated into a sequence of fixpoints that are often much easier to compute than the original one.  ...  Guided search applies hints to constrain the transition relation during fixpoint computations.  ...  Guided symbolic search applies constraints to the transition relation of the model to make the computation of fixpoints more efficient.  ... 
doi:10.1007/3-540-48683-6_21 fatcat:z2kfkg4syrbklb7zn7g2ybgmsy

The Magic of Pushing Extrema into Recursion: Simple, Powerful Datalog Programs

Carlo Zaniolo, Mohan Yang, Ariyam Das, Matteo Interlandi
2016 Alberto Mendelzon Workshop on Foundations of Data Management  
Complex algorithms can now be specified via simpler programs, and then implemented via optimized rules that use min and max aggregates in the seminaive fixpoint computation to achieve safe and efficient  ...  This optimization produces an efficient operational semantics for the goals declaratively specified by the original program that is stratified with respect to negation and aggregates.  ...  The perfect model of a stratified program is unique and can be computed using an iterated fixpoint computation, whereby the least fixpoint is computed starting at the bottom stratum and moving up to higher  ... 
dblp:conf/amw/ZanioloYDI16 fatcat:rc4pblp6nre3plkzqqqgdit25q

Action Language Verifier, Extended [chapter]

Tuba Yavuz-Kahveci, Constantinos Bartzis, Tevfik Bultan
2005 Lecture Notes in Computer Science  
Other extensions to ALV include several techniques to improve the efficiency of fixpoint computations such as marking heuristic and dependency analysis, and automated counting abstraction for verification  ...  Action Language Verifier uses several heuristics to achieve convergence: 1) Truncated fixpoint computations to compute lower bounds for least fixpoints and upper bounds for greatest fixpoints, 2) Widening  ... 
doi:10.1007/11513988_40 fatcat:q3ei4xi2pne6jew7rw5qwre4ly

Towards a New Step of Logic Paradigm [chapter]

Kazuhiro FUCHI
1990 Deductive and Object-Oriented Databases  
Nishio (Editors) It is desirable to answer queries posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing.  ...  In this formalism, the resolution-based methods are viewed as computing a fixpoint on answers and queries.  ...  In Section 3, we show how rules in tended for bottom-up computation can be used for specifying fixpoint procedures.  ... 
doi:10.1016/b978-0-444-88433-6.50008-3 fatcat:jgqxvfczlvgargtfqxaz6engrm

Symbolic guided search for CTL model checking

Roderick Bloem, Kavita Ravi, Fabio Somenzi
2000 Proceedings of the 37th conference on Design automation - DAC '00  
In this work, we show how hints can be used in the computation of nested fixpoints.  ...  We show how to use hints to obtain overapproximations useful for greatest fixpoints, and we present the first results for backward search.  ...  Notice that computing the least fixpoint under the original transition relation starting from the results obtained with the approximations may be dramatically more efficient than computing it from scratch  ... 
doi:10.1145/337292.337306 dblp:conf/dac/BloemRS00 fatcat:5re4jlsm7zec5fwd3glnb6ibam

Query Evaluation in Recursive Databases: Bottom-up and Top-down Reconciled [chapter]

François Bry
1990 Deductive and Object-Oriented Databases  
It is desirable to answer queries' posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing.  ...  Examining efficient implementations of the Backward Fixpoint Procedure, we investigate a technique called specialization.  ...  In this formalism, the resolution-based methods are viewed as computing a fixpoint on answers and queries.  ... 
doi:10.1016/b978-0-444-88433-6.50010-1 fatcat:iqqylekna5gfrmm54t7sz3jzim

Decoupling the ascending and descending phases in Abstract Interpretation [article]

Vincenzo Arceri and Isabella Mastroeni and Enea Zaffanella
2022 arXiv   pre-print
Interpretation approximates the semantics of a program by mimicking its concrete fixpoint computation on an abstract domain 𝔸.  ...  The abstract (post-) fixpoint computation is classically divided into two phases: the ascending phase, using widenings as extrapolation operators to enforce termination, is followed by a descending phase  ...  iteration [20, 21] so as to compute the exact abstract fixpoint.  ... 
arXiv:2206.10893v1 fatcat:i6h3k6zgojd7hoiwhblc7z3xmu

Query evaluation in recursive databases: bottom-up and top-down reconciled

François Bry
1990 Data & Knowledge Engineering  
It is desirable to answer queries' posed to deductive databases by computing fixpoints because such computations are directly amenable to set-oriented fact processing.  ...  Examining efficient implementations of the Backward Fixpoint Procedure, we investigate a technique called specialization.  ...  In this formalism, the resolution-based methods are viewed as computing a fixpoint on answers and queries.  ... 
doi:10.1016/0169-023x(90)90017-8 fatcat:uthlb7gvcbdvxpwkxdttaea6lu

An algebraic formulation of the aggregative closure query

Uchang Park
1996 Theoretical Computer Science  
So we can verify the existence of the fixpoint by the suggested conditions. The naive algorithm is proposed as a computational semantics for the aggregative closure problem.  ...  This study also proves that for an aggregative closure problem the semi-naive algorithm is computationally equivalent to the naive algorithm when the aggregate product operator is distributive over aggregate  ...  By the monotonicity of the (9 operator, the computation reaches a fixpoint.  ... 
doi:10.1016/0304-3975(95)00081-x fatcat:mpayhwnmvzhepkukpsl3xqcthi

Widening Arithmetic Automata [chapter]

Constantinos Bartzis, Tevfik Bultan
2004 Lecture Notes in Computer Science  
Given a widening operator one can compute an upper approximation of a least fixpoint in finite number of steps even if the least fixpoint is uncomputable.  ...  Model checking of infinite state systems is undecidable, therefore, there are instances for which fixpoint computations used in infinite state model checkers do not converge.  ...  Once again the exact fixpoint computation does not converge.  ... 
doi:10.1007/978-3-540-27813-9_25 fatcat:uavlqd4x2nd47gisc2fn77rplq
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