Modal Semirings Revisited

Desharnais, Jules; Struth, Georg

doi:10.1007/978-3-540-70594-9_19

Cited by 18 publications

(42 citation statements)

References 15 publications

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“…Domain algebras provide an elegant, one-sorted formalism for automated reasoning about program and system verification, see [DS08a,DS08b] and [HM11] for details and further motivation. The algebraic behaviour of domain algebras have been investigated, e.g.…”

Section: Introductionmentioning

confidence: 99%

Ordered domain algebras

Hirsch

Mikulás

2013

Journal of Applied Logic

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Section: Introductionmentioning

confidence: 99%

Ordered domain algebras

Hirsch

Mikulás

2013

Journal of Applied Logic

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“…Recent work already investigated the automation of computational logics [14], of relational reasoning [17], of rewriting and termination analysis [32,33], and of hybrid system analysis [13]. It has also been shown that ATP can be very helpful in developing consistent irredundant specifications and axiomatisations of algebraic theories [11,10]. This paper investigates the automated verification of refinement laws.…”

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confidence: 99%

Automated verification of refinement laws

Höfner

Struth

Sutcliffe

2009

Ann Math Artif Intell

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Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs.

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“…hold [DS08]. Multiplying the last axiom by x on both sides and applying (D1) shows that every domain semiring is an idempotent semiring.…”

Section: Domain Semiringsmentioning

confidence: 99%

“…Proofs of the previous lemma with an automated theorem prover (such as Prover9 [McC07]) can also be found in [DS08].…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…The reason is that arbitrary semiring elements are intended to model the actions of some program or transition system whereas the elements of the Boolean subalgebra model the states of that system. This approach has recently been generalised to a one-sorted setting [DS08] and we base our considerations on this simpler and more flexible approach.…”

Section: Introductionmentioning

confidence: 99%

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The Structure of the One-Generated Free Domain Semiring

Jipsen

Struth

Relations and Kleene Algebra in Computer Science

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Abstract. This note gives an explicit construction of the one-generated free domain semiring. In particular it is proved that the elements can be represented uniquely by finite antichains in the poset of finite strictly decreasing sequences of nonnegative integers. It is also shown that this domain semiring can be represented by sets of binary relations with union, composition and relational domain as operations.

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Modal Semirings Revisited

Cited by 18 publications

References 15 publications

Ordered domain algebras

Ordered domain algebras

Automated verification of refinement laws

The Structure of the One-Generated Free Domain Semiring

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