منابع مشابه
Constraint Satisfaction Problems around Skolem Arithmetic
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glaßer et al. [17] in the context of CSPs and settle the major open question from that paper, finding a certain satisfaction problem on circuits to be decidable. This we prove using the decidability of Skolem Arithmetic. We continue by studying first-order expans...
متن کاملAlgorithms for Ordinal Arithmetic
Proofs of termination are essential for establishing the correct behavior of computing systems. There are various ways of establishing termination, but the most general involves the use of ordinals. An example of a theorem proving system in which ordinals are used to prove termination is ACL2. In ACL2, every function defined must be shown to terminate using the ordinals up to 0. We use a compac...
متن کاملOrdinal Arithmetic in ACL2
Ordinals form the basis for termination proofs in ACL2. Currently, ACL2 uses a rather inefficient representation for the ordinals up to 0 and provides limited support for reasoning about them. We present algorithms for ordinal arithmetic on an exponentially more compact representation than the one used by ACL2. The algorithms have been implemented and numerous properties of the arithmetic opera...
متن کاملOrdinal Arithmetic with List Structures
We provide a set of \natural" requirements for well-orderings of (binary) list structures. We show that the resultant order-type is the successor of the rst critical epsilon number. The checker has to verify that the process comes to an end. Here again he should be assisted by the programmer giving a further de nite assertion to be veri ed. This may take the form of a quantity which is asserted...
متن کاملInteractive Realizability for Classical Peano Arithmetic with Skolem Axioms
Interactive realizability is a computational semantics of classical Arithmetic. It is based on interactive learning and was originally designed to interpret excluded middle and Skolem axioms for simple existential formulas. A realizer represents a proof/construction depending on some state, which is an approximation of some Skolem functions. The realizer interacts with the environment, which ma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2007
ISSN: 0168-0072
DOI: 10.1016/j.apal.2006.07.003