Solving systems of set constraints

It is shown that systems of set constraints that use all the standard set operations, especially unrestricted union and complement, can be solved. The centerpiece of the development is an algorithm that incrementally transforms a system of constraints while preserving the set of solutions. Eventually, either the system is shown to be inconsistent or all solutions can be exhibited. Most of the work is in proving that if this algorithm does not discover an inconsistency, then the system has a solution. This is done by showing that the system of constraints generated by the algorithm can be transformed into an equivalent set of equations that are guaranteed to have a solution. These equations are essentially tree automata.<<ETX>>

[1]  Prateek Mishra,et al.  Declaration-free type checking , 1985, POPL.

[2]  Ernst L. Leiss,et al.  On Equations for Regular Languages, Finite Automata, and Sequential Networks , 1980, Theor. Comput. Sci..

[3]  Neil D. Jones,et al.  Flow analysis and optimization of LISP-like structures , 1979, POPL.

[4]  Prateek Mishra,et al.  Towards a Theory of Types in Prolog , 1984, SLP.

[5]  Thom W. Frühwirth,et al.  Logic programs as types for logic programs , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[6]  Alexander Aiken,et al.  Static type inference in a dynamically typed language , 1991, POPL '91.

[7]  Alexander Aiken,et al.  Implementing Regular Tree Expressions , 1991, FPCA.

[8]  Helmut Seidl.  Deciding Equivalence of Finite Tree Automata , 1990, SIAM J. Comput..

[9]  Giora Slutzki,et al.  Alternating Tree Automata , 1983, Theor. Comput. Sci..

[10]  John C. Reynolds,et al.  Automatic computation of data set definitions , 1968, IFIP Congress.

[11]  M. Rabin.  Decidability of second-order theories and automata on infinite trees. , 1969 .

[12]  Joxan Jaffar,et al.  A decision procedure for a class of set constraints , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[13]  Gilberto Filé.  Tree Automata and Logic Programs , 1985, STACS.

[14]  Nevin Charles Heintze,et al.  Set based program analysis , 1992 .

[15]  M. Rabin.  Decidability of second-order theories and automata on infinite trees , 1968 .

[16]  Joxan Jaffar,et al.  A finite presentation theorem for approximating logic programs , 1989, POPL '90.