Deciding Linear Inequalities by Computing Loop Residues

V R Pratt has shown that the real and integer feastbdlty of sets of linear mequallUes of the form x _< y + c can be decided quickly by examining the loops m certain graphs Pratt's method is generahzed, first to real feaslbdlty of mequahues m two variables and arbitrary coefficients, and ultimately to real feaslbdlty of arbitrary sets of hnear mequahtles The method is well suited to apphcatlons m program verification

[1]  Ralph E. Gomory,et al.  An algorithm for integer solutions to linear programs , 1958 .

[2]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[3]  Robert S. Boyer,et al.  Computer Proofs of Limit Theorems , 1971, IJCAI.

[4]  R. D. Lee.  An application of mathematical logic to the integer linear programming problem , 1972, Notre Dame J. Formal Log..

[5]  Robert E. Tarjan,et al.  Enumeration of the Elementary Circuits of a Directed Graph , 1972, SIAM J. Comput..

[6]  W. W. Bledsoe,et al.  A Man-Machine Theorem-Proving System , 1973, IJCAI.

[7]  L. Peter Deutsch.  An interactive program verifier , 1973 .

[8]  Karl N. Levitt,et al.  Reasoning about programs , 1973, POPL '73.

[9]  Robert E. Tarjan,et al.  Bounds on Backtrack Algorithms for Listing Cycles, Paths, and Spanning Trees , 1975, Networks.

[10]  Norihisa Suzuki.  Verifying programs by algebraic and logical reduction , 1975 .

[11]  Donald B. Johnson,et al.  Finding All the Elementary Circuits of a Directed Graph , 1975, SIAM J. Comput..

[12]  W. Bledsoe.  A new method for proving certain Presburger formulas , 1975, IJCAI 1975.

[13]  Donald I. Good,et al.  An interactive program verification system , 1975 .

[14]  Norihisa Suzuki,et al.  Verifying programs by algebraic and logical reduction , 1975, Reliable Software.

[15]  Narsingh Deo,et al.  On Algorithms for Enumerating All Circuits of a Graph , 1976, SIAM J. Comput..

[16]  Robert E. Shostak,et al.  On the SUP-INF Method for Proving Presburger Formulas , 1977, JACM.

[17]  Vaughan R. Pratt,et al.  A Proof-Checker for Dynamic Logic , 1977, IJCAI.

[18]  Bengt Aspvall,et al.  A Polynomial Time Algorithm for Solving Systems of Linear Inequalities with Two Variables per Inequality , 1980, SIAM J. Comput..

[19]  L. Khachiyan.  Polynomial algorithms in linear programming , 1980 .