Sets with Cardinality Constraints in Satisfiability Modulo Theories
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Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010
Applications in software verification and interactive theorem proving often involve reasoning about sets of objects. Cardinality constraints on such collections also arise in these scenarios. Multisets arise for analogous reasons as sets: abstracting the c ...
Motivated by the problem of deciding verification conditions for the verification of functional programs, we present new decision procedures for automated reasoning about functional lists. We first show how to decide in NP the satisfiability problem for lo ...
Automated termination provers often use the following schema to prove that a program terminates: construct a relational abstraction of the program's transition relation and then show that the relational abstraction is well-founded. The focus of current too ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2011
Our goal is to identify families of relations that are useful for reasoning about software. We describe such families using decidable quantifier-free classes of logical constraints with a rich set of operations. A key challenge is to define such classes of ...
Techniques such as verification condition generation, predicate abstraction, and expressive type systems reduce software verification to proving formulas in expressive logics. Programs and their specifications often make use of data structures such as sets ...
We explore the problem of automated reasoning about the non-disjoint combination of theories that share set variables and operations. We prove a combination theorem and apply it to show the decidability of the satisfiability problem for a class of formulas ...
Motivated by applications in software verification, we explore automated reasoning about the non-disjoint combination of theories of infinitely many finite structures, where the theories share set variables and set operations. We prove a combination theore ...
Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier- ...
We explore the problem of automated reasoning about the non-disjoint combination of logics that share set variables and operations. We prove a general combination theorem, and apply it to show the decidability for the quantifier-free combination of formula ...
