L. Fribourg, "Mixing list recursion and arithmetic", Proc. Seventh Symp. on Logic in Computer Science, 1992. Home/Search Document Details and Download
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Extending Decision Procedures with Induction Schemes - Kapur, Subramaniam (2000) (Correct)
....how these examples can be done using the interaction of the theorem prover and the decision procedure. In this paper we have focussed on automatically deciding the validity of such conjectures. Most of the examples described there can be automatically decided using the proposed approach. Fribourg [4] showed that properties of certain recursive predicates over lists expressed as logic programs along with numbers, can be decided. Most of the properties established there can be formulated as equational definitions and decided using the proposed approach. The procedure in [4] used bottom up ....
....approach. Fribourg [4] showed that properties of certain recursive predicates over lists expressed as logic programs along with numbers, can be decided. Most of the properties established there can be formulated as equational definitions and decided using the proposed approach. The procedure in [4] used bottom up evaluation of logic programs which need not terminate if successor operation over numbers is included. The proposed approach does not appear to have this limitation. Gupta s dissertation [1] was an attempt to integrate (a limited form of) inductive reasoning with a decision ....
L. Fribourg, "Mixing list recursion and arithmetic", Proc. Seventh Symp. on Logic in Computer Science, 1992.
A Proof Method based on Folding Lemmas: Applications to.. - Staffan Bonnier Self-citation (Fribourg) (Correct)
....Linkoping University, Sweden LIENS 92 28 December A Proof Method based on Folding Lemmas: Applications to Algorithm Correctness Staffan Bonnier 1 , Laurent Fribourg L.i.e.N. S (URA 1327 CNRS) 45 rue d Ulm, 75005 Paris France e mail: bonnier,fribourg dmi.ens.fr Abstract In [Fri92] a proof method was developed for proving arithmetic consequences of Horn clause programs defined over integer lists and integers. To be applicable, the method requires the recursion schemes of all predicates involved to be compatible. This is to guarantee a sequence of unfold transformations to ....
....are constructed. The proof then proceeds using the old method, and the theorem is proved with the lemmas as hypotheses. The method is illustrated by proving correctness criteria for Boyer and Moore s string matching algorithm and for Dijkstra s descending subsequence algorithm. 1 Introduction In [Fri92], a method was developed for proving implications of the form: p 1 (L; X 1 ) p n (L; X n ) a(X 1 : X n ) where L is a list variable, each X i is a vector of integer variables, and a(X 1 : X n ) is an arithmetic formula. The method works by transforming the hypothesis of the ....
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L. Fribourg. Mixing List Recursion and Arithmetic. In Proc. 7th Symp. on Logic in Computer Science, pages 419--429, Santa Cruz, 1992. IEEE.
Bottom-up Evaluation of Datalog Programs with Arithmetic.. - Laurent Fribourg (1992) (1 citation) Self-citation (Fribourg) (Correct)
....variables, but no function symbol) 4] We describe in this paper a bottom up evaluation process for Datalog programs (or logic programs) whose variables are interpreted as integers. Our initial motivation was to use such a process in order to prove formulas combining lists and linear arithmetic [10]. Let us illustrate this point with an example which corresponds to an adaptation of the BoyerMoore Majority Algorithm (see [24] This algorithm determines the element of a list that occurs more than half times the size of the list, if such an element exists. Let p(L; v; w; x; y; z) be an atom ....
.... logic program defining a predicate of the form p(L; x; y; z) where L is a variable denoting a list of integers, and x; y; z are variables denoting integers, it is often possible to transform the atom p(L; x; y; z) into an atom of the form p 0 (x; y; z) defined only over integer arguments (see [10]) The bottom up evaluation of p 0 (x; y; z) then yields an arithmetic relation (x; y; z) that also holds for p(L; x; y; z) generating the lemma: p(L; x; y; z) x; y; z) In the motivation section, we have thus sketched out how to generate the lemma p(L; v; w; x; y; z) v 6= w = z y ....
L. Fribourg. "Mixing List Recursion and Arithmetic". Proc. 7th IEEE Symp. on Logic in Computer Science, Santa Cruz, 1992, pp. 419-429.
Concurrent Constraint Automata - Fribourg, Peixoto (1993) (4 citations) Self-citation (Fribourg) (Correct)
.... automata AUT and AUT 0 , Rec(AUT ) Rec(AUT 0 ) iff 8L 8S 8S 0 ( aut(L; S) aut 0 comp (L; S 0 ) S 0 6= s 0 error ) We now describe a method to decide the validity of: aut(L; S) aut 0 comp (L; S 0 ) S 0 6= s 0 error ( This is done following the steps below (cf. [6]) 1. Construct the program Pi inter associated with the intersection automaton of AUT and AUT 0 comp . 2. Construct the program Pi 0 inter obtained removing the list argument L and the action parameters M from the clauses of Pi inter . 3. Compute the output of the bottom up evaluation ....
L. Fribourg. "Mixing List Recursion and Arithmetic", Proc. 7th IEEE Symp. on Logic in Computer Science, Santa Cruz, 1991, pp. 419-429.
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