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Cham : Springer International Publishing AG, 2021

1 online resource (587 pages)

ISBN 9783030719951 (electronic bk.)

ISBN 9783030719944

Theoretical Computer Science and General Issues Ser. ; v.12650

Print version: Kiefer, Stefan Foundations of Software Science and Computation Structures Cham : Springer International Publishing AG,c2021 ISBN 9783030719944

Intro -- ETAPS Foreword -- Preface -- Organization -- Contents -- Constructing a universe for the setoid model -- 1 Introduction -- 1.1 Related work -- 2 MLTT Prop -- 2.1 Formalization -- 3 Setoid model -- 3.1 Setoid model as a CwF -- 3.2 Setoid Type Theory -- 4 Universe of setoids -- 4.1 Inductive-recursive universes -- 4.2 Inductive-recursive setoid universe -- 4.3 Inductive-inductive setoid universe -- 4.4 Inductive setoid universe -- 5 Conclusions and further work -- References -- Nominal Equational Problems -- 1 Introduction -- 2 Background -- 3 Nominal Equational Problems -- 4 A rule-based procedure -- 4.1 Simplification Rules -- 4.2 Soundness and Preservation of Solutions -- 4.3 Termination -- 5 Nominal Equational Solved Forms -- 6 Conclusion -- References -- Finding Cut-Offs in Leaderless Rendez-Vous Protocols is Easy -- 1 Introduction -- 2 Preliminaries -- 3 The cut-off problem for acyclic Petri nets -- 3.1 Characterizing acyclic systems with cut-offs -- 3.2 Polynomial time algorithm -- 4 The Scaling and Insertion lemmas -- 4.1 The Scaling Lemma -- 4.2 The Insertion Lemma -- 5 Polynomial time algorithm for the general case -- 5.1 Characterizing systems with cut-offs -- 5.2 Polynomial time algorithm -- 6 Symmetric rendez-vous protocols -- 7 Symmetric protocols with leaders -- 7.1 A non-deterministic polynomial time algorithm -- References -- Fixpoint Theory - Upside Down -- 1 Introduction -- 2 Lattices and MV-Algebras -- 3 Non-expansive Functions and Their Approximations -- 4 Proof Rules -- 5 (De)Composing Functions and Approximations -- 6 Applications -- 6.1 Termination Probability -- 6.2 Behavioural Metrics for Probabilistic Automata -- 6.3 Bisimilarity -- 7 Simple Stochastic Games -- 8 Conclusion -- References -- Most of’’ leads to undecidability: Failure of adding frequencies to LTL -- 1 Introduction -- 1.1 Related work.

2 Preliminaries -- 3 Playing with Half Operator -- 4 Undecidability of LTL extensions -- 4.1 "Half of" meets the halting problem -- Fact 5 -- Fact 6 -- 6.1 Undecidability of model-checking -- 6.2 Most-Frequent Letter and Undecidability -- 6.3 Most-Frequent Letter: the reduction -- 7 Decidable variants -- 8 Two-Variable First-Order Logic with Majority -- 9 Conclusions -- References -- Combining Semilattices and Semimodules -- 1 Introduction -- 2 (Weak) Distributive laws -- 3 The Powerset and Semimodule Monads -- 4 The Weak Distributive Law e : SP → PS -- 5 The Weak Lifting of P to EM(S) -- 5.1 Proof of Theorem 24 -- 6 The Composite Monad: an Algebraic Presentation -- 7 Conclusions: Related and Future Work -- References -- One-way Resynchronizability of Word Transducers -- 1 Introduction -- 2 Preliminaries -- 3 One-way resynchronizability -- 3.1 Regular resynchronizers -- 3.2 Main result -- 4 Proof overview for Theorem 1 -- 4.1 Flows and inversions -- 4.2 Dominant output intervals -- 5 Proof of Theorem 1 -- 6 Proof overview of Theorem 2 -- 7 Complexity -- 8 Conclusions -- References -- Fair Refinement for Asynchronous Session Types -- 1 Introduction -- 2 Refinement for Asynchronous Session Types -- 2.1 Preliminaries: Asynchronous Session Types -- 2.2 Fair Refinement for Asynchronous Session Types -- 2.3 Controllability for Asynchronous Session Types -- 3 Fair Asynchronous Session Subtyping -- 4 A Sound Algorithm for Fair Asynchronous Subtyping -- 5 Implementation -- 6 Related and Future Work -- References -- Running Time Analysis of Broadcast Consensus Protocols -- 1 Introduction -- 2 Preliminaries -- 3 Example: Majority -- 4 Comparison with other Models -- 4.1 Non-Deterministic Broadcast Protocols -- 4.2 Population Protocols -- 5 Protocols for Presburger Arithmetic -- 5.1 Linear Inequalities -- 5.2 Modulo Predicates and Boolean Combinations.

4 Encoding regular expressions and automata.

6 Protocols for all Predicates in ZPL -- References -- Leafy automata for higher-order concurrency -- 1 Introduction -- 2 Finitary Idealized Concurrent Algol (FICA) -- 3 Game semantics -- 4 Leafy automata -- 5 Local leafy automata (LLA) -- 6 From FICA to LA -- 7 Local FICA -- 8 From LA to FICA -- 9 Conclusion and further work -- References -- Factorization in Call-by-Name and Call-by-Value Calculi via Linear Logic -- 1 Introduction -- 2 Background in Abstract Rewriting -- 3 n-calculi: CbN, CbV, and bang -- 3.1 Call-by-Name and Call-by-Value n-calculi -- 3.2 Bang calculi -- 3.3 CbN and CbV translations into the bang calculus -- 4 The least-level strategy -- 4.1 Least-level reduction in bang calculi -- 4.2 Least-level for a bang calculus: examples. -- 4.3 Least-level for CbN and CbV n-calculi -- 5 Embedding of CbN and CbV by level -- 6 Least-level factorization via bang calculus -- 6.1 Factorization of →b! in a bang calculus -- 6.2 Pure calculi and least-level normalization -- 6.3 Least-level Factorization, Modularly -- 7 Case study: non-deterministic n-calculi -- 8 Conclusions and Related Work -- References -- Generalized Bounded Linear Logic and its Categorical Semantics -- 1 Introduction -- 2 Generalized Bounded Linear Logic -- 2.1 Indexing 2-Category -- 2.2 Formulas and Proofs -- 2.3 Complexity of Cut-Elimination in GBLL -- 3 Translation from Constrained BLL -- 3.1 Resource Polynomials and Constraints -- 3.2 Formulas and Inference Rules of CBLL -- 3.3 Translation into GBAL+ -- 4 Categorical Semantics for GBLL -- 4.1 Semantics of GBLL -- 4.2 Construction of an Indexed Linear Exponential Comonad -- 4.3 GBLL Semantics by Realizability Category -- 5 Conclusion and Related Work -- References -- Focused Proof-search in the Logic of Bunched Implications -- 1 Introduction -- 2 Re-presentations of BI -- 2.1 Traditional Syntax -- 2.2 Sequent Calculus.

2 Preliminaries -- 3 Playing with Half Operator -- 4 Undecidability of LTL extensions -- 4.1 "Half of" meets the halting problem -- Fact 5 -- Fact 6 -- 6.1 Undecidability of model-checking -- 6.2 Most-Frequent Letter and Undecidability -- 6.3 Most-Frequent Letter: the reduction -- 7 Decidable variants -- 8 Two-Variable First-Order Logic with Majority -- 9 Conclusions -- References -- Combining Semilattices and Semimodules -- 1 Introduction -- 2 (Weak) Distributive laws -- 3 The Powerset and Semimodule Monads -- 4 The Weak Distributive Law e : SP → PS -- 5 The Weak Lifting of P to EM(S) -- 5.1 Proof of Theorem 24 -- 6 The Composite Monad: an Algebraic Presentation -- 7 Conclusions: Related and Future Work -- References -- One-way Resynchronizability of Word Transducers -- 1 Introduction -- 2 Preliminaries -- 3 One-way resynchronizability -- 3.1 Regular resynchronizers -- 3.2 Main result -- 4 Proof overview for Theorem 1 -- 4.1 Flows and inversions -- 4.2 Dominant output intervals -- 5 Proof of Theorem 1 -- 6 Proof overview of Theorem 2 -- 7 Complexity -- 8 Conclusions -- References -- Fair Refinement for Asynchronous Session Types -- 1 Introduction -- 2 Refinement for Asynchronous Session Types -- 2.1 Preliminaries: Asynchronous Session Types -- 2.2 Fair Refinement for Asynchronous Session Types -- 2.3 Controllability for Asynchronous Session Types -- 3 Fair Asynchronous Session Subtyping -- 4 A Sound Algorithm for Fair Asynchronous Subtyping -- 5 Implementation -- 6 Related and Future Work -- References -- Running Time Analysis of Broadcast Consensus Protocols -- 1 Introduction -- 2 Preliminaries -- 3 Example: Majority -- 4 Comparison with other Models -- 4.1 Non-Deterministic Broadcast Protocols -- 4.2 Population Protocols -- 5 Protocols for Presburger Arithmetic -- 5.1 Linear Inequalities -- 5.2 Modulo Predicates and Boolean Combinations.

2.3 Nested Calculus -- 3 A Focused System -- 3.1 Polarisation -- 3.2 Focused Calculus -- 3.3 Completeness of fBI -- 4 Conclusion -- References -- Interpolation and Amalgamation for Arrays with MaxDiff -- 1 Introduction -- 2 Formal Preliminaries -- 3 Arrays with MaxDiff -- 3.1 Our roadmap -- 4 Embeddings -- 5 Amalgamation -- 6 Satisfiability -- 7 An interpolation algorithm -- 8 When indexes are just a total order -- 9 Conclusions and further work -- References -- Adjoint Reactive GUI Programming -- Introduction -- The Language -- Formal Calculus -- Semantics -- Related and Future Work -- References -- On the Expressiveness of Buchi Arithmetic -- 1 Introduction -- 2 Preliminaries -- 3 The inexpressiveness of existential Buchi arithmetic -- 4 Expressive completeness of the ∑2-fragment of Buchi arithmetic -- 5 Existential Buchi arithmetic defines regular languages of polynomial growth -- 6 Conclusion -- References -- Parametricity for Primitive Nested Types -- 1 Introduction -- 2 The Calculus -- 2.1 Types -- 2.2 Terms -- 3 Interpreting Types -- 3.1 Interpreting Types as Sets -- 3.2 Interpreting Types as Relations -- 4 The Identity Extension Lemma -- 5 Interpreting Terms -- 6 Free Theorems for Nested Types -- 6.1 Consequences of Naturality -- 6.2 The Abstraction Theorem -- 7 Conclusion and Directions for Future Work -- References -- The Spirit of Node Replication -- 1 Introduction -- 2 A Calculus for Node Replication -- 3 Operational Properties -- 4 Encoding Evaluation Strategies -- 4.1 Call-by-name -- 4.2 Call-by-need -- 5 A Type System for the nR-calculus -- 6 Observational Equivalence -- 7 Related Works and Conclusion -- References -- Nondeterministic and co-Nondeterministic Implies Deterministic, for Data Languages -- 1 Introduction -- 2 Data languages and register automata -- 3 Examples -- 4 Main results -- 5 Orbit-finite automata.

6 Proof of Theorem 1 -- 6.1 Examples -- 6.2 Proof of Lemma 1 -- 7 Application to Unambiguous Register Automata -- 8 Proof of Theorem 2 -- 9 Final remarks -- References -- Certifying Inexpressibility -- 1 Introduction -- 2 Preliminaries -- 2.1 Transducers and Realizability -- 2.2 Automata -- 3 Refuting DBW-Recognizability -- 3.1 Complexity -- 3.2 Certifying DBW-Refutation -- 4 Separability and Approximations -- 4.1 Refuting Separability -- 4.2 Certificate-Guided Approximation -- 5 Other Classes of Deterministic Automata -- 6 Discussion and Directions for Future Research -- References -- A General Semantic Construction of Dependent Refinement Type Systems, Categorically -- 1 Introduction -- 2 Preliminaries -- 3 Lifting SCCompCs and Fibred Coproducts -- 3.1 Lifting SCCompCs -- 3.2 Lifting Fibred Coproducts -- 4 Lifting Monads on SCCompCs -- 5 Soundness -- 5.1 Underlying Type System -- 5.2 Predicate Logic -- 5.3 Refinement Type System -- 5.4 Semantics -- 6 Toward Recursion in Refinement Type Systems -- 6.1 Conway Operators -- 6.2 Recursion in the Underlying Type System -- 7 Related Work -- 8 Conclusion and Future Work -- References -- Simple Stochastic Games with Almost-Sure Energy-Parity Objectives are in NP and coNP -- 1 Introduction -- 2 Preliminaries -- 3 Characterizing Energy-Parity via Gain and Bailout -- 4 Bailout -- 5 Gain -- 6 The Main Results -- 7 Conclusion and Outlook -- References -- Nondeterministic Syntactic Complexity -- 1 Introduction -- 2 Preliminaries -- 3 Duality Theory of Semilattice Automata -- 4 Boolean Representations and Subatomic NFAs -- 5 Applications -- 5.1 Unary languages -- 5.2 Languages with a canonical state-minimal nfa -- 6 Conclusion and Future Work -- References -- A String Diagrammatic Axiomatisation of Finite-State Automata -- 1 Introduction -- 2 Syntax and semantics -- 3 Equational theory.

6 Protocols for all Predicates in ZPL -- References -- Leafy automata for higher-order concurrency -- 1 Introduction -- 2 Finitary Idealized Concurrent Algol (FICA) -- 3 Game semantics -- 4 Leafy automata -- 5 Local leafy automata (LLA) -- 6 From FICA to LA -- 7 Local FICA -- 8 From LA to FICA -- 9 Conclusion and further work -- References -- Factorization in Call-by-Name and Call-by-Value Calculi via Linear Logic -- 1 Introduction -- 2 Background in Abstract Rewriting -- 3 n-calculi: CbN, CbV, and bang -- 3.1 Call-by-Name and Call-by-Value n-calculi -- 3.2 Bang calculi -- 3.3 CbN and CbV translations into the bang calculus -- 4 The least-level strategy -- 4.1 Least-level reduction in bang calculi -- 4.2 Least-level for a bang calculus: examples. -- 4.3 Least-level for CbN and CbV n-calculi -- 5 Embedding of CbN and CbV by level -- 6 Least-level factorization via bang calculus -- 6.1 Factorization of →b! in a bang calculus -- 6.2 Pure calculi and least-level normalization -- 6.3 Least-level Factorization, Modularly -- 7 Case study: non-deterministic n-calculi -- 8 Conclusions and Related Work -- References -- Generalized Bounded Linear Logic and its Categorical Semantics -- 1 Introduction -- 2 Generalized Bounded Linear Logic -- 2.1 Indexing 2-Category -- 2.2 Formulas and Proofs -- 2.3 Complexity of Cut-Elimination in GBLL -- 3 Translation from Constrained BLL -- 3.1 Resource Polynomials and Constraints -- 3.2 Formulas and Inference Rules of CBLL -- 3.3 Translation into GBAL+ -- 4 Categorical Semantics for GBLL -- 4.1 Semantics of GBLL -- 4.2 Construction of an Indexed Linear Exponential Comonad -- 4.3 GBLL Semantics by Realizability Category -- 5 Conclusion and Related Work -- References -- Focused Proof-search in the Logic of Bunched Implications -- 1 Introduction -- 2 Re-presentations of BI -- 2.1 Traditional Syntax -- 2.2 Sequent Calculus.

001895464

express

(Au-PeEL)EBL6524970

(MiAaPQ)EBC6524970

(OCoLC)1244535767