| Entrambe le parti precedenti la revisioneRevisione precedenteProssima revisione | Revisione precedente |
| magistraleinformatica:mpp:start [07/09/2025 alle 11:04 (4 settimane fa)] – [Lectures (1st part)] Roberto Bruni | magistraleinformatica:mpp:start [02/10/2025 alle 12:36 (3 giorni fa)] (versione attuale) – [Lectures (1st part)] Roberto Bruni |
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| ====== Models for Programming Paradigms ====== | ====== Models for Programming Paradigms ====== |
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| {{:magistraleinformatica:psc:psc.png?250 | }} | {{:magistraleinformatica:mpp:logo-van-gogh-like.png?150 | }} |
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| **MPP 2025/26 (0077A, 9 CFU)** | **MPP 2025/26 (0077A, 9 CFU)** |
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| ^ N ^ Date ^^ Time ^ Room ^ Lecture notes ^ Links ^ | ^ N ^ Date ^^ Time ^ Room ^ Lecture notes ^ Links ^ |
| | 1 | Tue | 16/09 | 16:00-18:00 | C1 | 01 - Introduction to the course\\ \\ 02 - Preliminaries:\\ //from syntax to semantics, the role of formal semantics, SOS approach, small-step operational semantics, big-step operational semantics// | | | | 1 | Tue | 16/09 | 16:00-18:00 | C1 | {{ :magistraleinformatica:mpp:2025-09-16_-_01_-_intro.pdf |01 - Introduction to the course}} | | |
| | 2 | Thu | 18/09 | 09:00-11:00 | L1 | 02 - Preliminaries (ctd):\\ //denotational semantics, compositionality principle, normalisation, determinacy, consistency, equivalence, congruence//\\ \\ 03 - Unification:\\ //inference process, signatures, substitutions, most general than relation, unification problem// | | | | 2 | Thu | 18/09 | 09:00-11:00 | L1 | {{ :magistraleinformatica:mpp:2025-09-18_-_02_-_semantics.pdf |02 - Preliminaries}}:\\ //from syntax to semantics, the role of formal semantics, SOS approach, small-step operational semantics, big-step operational semantics, denotational semantics, compositionality principle, normalisation, determinacy, consistency, equivalence, congruence// | | |
| | 3 | Fri | 19/09 | 16:00-18:00 | L1 | 03 - Unification (ctd):\\ //unification problem, most general unifiers, unification algorithm//\\ \\ 04 - Logical systems:\\ //logical systems, derivations, theorems, logic programs, goal-oriented derivations// | | | | 3 | Fri | 19/09 | 16:00-18:00 | L1 | Exercises\\ \\ {{ :magistraleinformatica:mpp:2025-09-19_-_03_-_unification.pdf |03 - Unification}}:\\ //inference process, signatures, substitutions, most general than relation, unification problem, most general unifiers, unification algorithm// | | |
| | 4 | | | | | Exercises:\\ //unification, goal-oriented derivations//\\ \\ 05 - Induction:\\ //precedence relation, infinite descending chains, well-founded relations, well-founded induction, mathematical induction, proof of induction principle, structural induction, termination of arithmetic expressions// | {{ :magistraleinformatica:psc:01_-_inference_-_2025.pdf |Exercises 01}}\\ {{ :magistraleinformatica:psc:2025-02-24_-_05a_-_induction.pdf |Lecture 05a}} | | | 4 | Tue | 23/09 | 16:00-18:00 | C1 | Exercises:\\ //unification, goal-oriented derivations//\\ \\ {{ :magistraleinformatica:mpp:2025-09-23_-_04_-_logic.pdf |04 - Logical systems}}:\\ //logical systems, derivations, theorems, logic programs, goal-oriented derivations// | | |
| | 5 | | | | | Exercises:\\ //induction//\\ \\ 05 - Induction (ctd.):\\ //determinacy of arithmetic expressions, many-sorted signatures, arithmetic and boolean expressions, structural induction over many-sorted signatures, termination of boolean expressions, memories, update operation, operational semantics of commands// | {{ :magistraleinformatica:psc:2025-03-04_-_05b_-_more_induction.pdf |Lecture 05b}} | | | 5 | Thu | 25/09 | 09:00-11:00 | L1 | {{ :magistraleinformatica:mpp:2025-09-25_-_05a_-_induction.pdf |05 - Induction}}:\\ //precedence relation, infinite descending chains, well-founded relations, well-founded induction, mathematical induction, proof of induction principle, structural induction, termination of arithmetic expressions, determinacy of arithmetic expressions, many-sorted signatures, arithmetic and boolean expressions, structural induction over many-sorted signatures, termination of boolean expressions, memories, update operation, operational semantics of commands// | | |
| | 6 | | | | | 05 - Induction (ctd.):\\ //divergence, rule for divergence, limits of structural induction, induction on derivations, rule induction, determinacy of commands// | {{ :magistraleinformatica:psc:2025-03-06_-_05c_-_rule_induction.pdf |Lecture 05c}} | | | 6 | Fri | 26/09 | 16:00-18:00 | L1 | Exercises:\\ //induction//\\ \\ {{ :magistraleinformatica:mpp:2025-09-26_-_05b_-_more_induction.pdf |05 - More induction}} (Structural Induction)://many-sorted signatures, arithmetic and boolean expressions, structural induction over many-sorted signatures, termination of boolean expressions, memories, update operation, operational semantics of commands// | | |
| | 7 | | | | | 06 - Equivalence:\\ //operational equivalence, concrete equivalences, parametric equivalences, equivalence and divergence//\\ \\ 07 - Induction and recursion:\\ //well-founded recursion, lexicographic precedence relation, Ackermann function, denotational semantics of arithmetic expressions, consistency of operational and denotational semantics for arithmetic expressions, fixpoint equations// | {{ :magistraleinformatica:psc:2025-03-07_-_06_-_equivalence.pdf |Lecture 06}}\\ {{ :magistraleinformatica:psc:2025-03-07_-_07_-_recursion.pdf |Lecture 07}} | | | 7 | Tue | 30/09 | 16:00-18:00 | C1 | Exercises:\\ //induction//\\ \\ {{ :magistraleinformatica:mpp:2025-09-30_-_05c_-_rule_induction.pdf |05 - More induction (Rule Induction)}}:\\ //divergence, rule for divergence, limits of structural induction, induction on derivations, rule induction, determinacy of commands// | | |
| | 8 | | | | | 08 - Partial orders and fixpoints:\\ //partial orders, Hasse diagrams, chains, least element, minimal element, bottom element, upper bounds, least upper bound, limits, complete partial orders, powerset completeness, prefix independence, CPO of partial functions, monotonicity// | {{ :magistraleinformatica:psc:2025-03-11_-_08a_-_cpo.pdf |Lecture 08a}}\\ {{ :magistraleinformatica:psc:2025-03-11_-_08b_-_kleene.pdf |Lecture 08b}} | | | 8 | Thu | 02/10 | 09:00-11:00 | L1 | {{ :magistraleinformatica:mpp:2025-10-02_-_06_-_equivalence.pdf |06 - Equivalence}}:\\ //operational equivalence, concrete equivalences, parametric equivalences, equivalence and divergence//\\ \\ {{ :magistraleinformatica:mpp:2025-10-02_-_07_-_recursion.pdf |07 - Induction and recursion}}:\\ //well-founded recursion, lexicographic precedence relation, Ackermann function, denotational semantics of arithmetic expressions, towards denotational semantics of commands// | | |
| | 9 | | | | | Exercises:\\ //induction, termination, determinacy, divergence//\\ \\ 08 - Partial orders and fixpoints (ctd.):\\ //continuity, Kleene's fixpoint theorem, McCarthy's 91 function// | {{ :magistraleinformatica:psc:02_-_properties-2025.pdf |Exercises 02}}\\ {{ :magistraleinformatica:psc:2025-03-11_-_08b_-_kleene.pdf |Lecture 08b}}\\ | | | 9 | Fri | 03/10 | 16:00-18:00 | L1 | 08 - Partial orders and fixpoints:\\ //consistency of operational and denotational semantics for arithmetic expressions, fixpoint equations, partial orders, Hasse diagrams, chains, least element, minimal element, bottom element, upper bounds, least upper bound, limits, complete partial orders, powerset completeness, prefix independence, CPO of partial functions, monotonicity//\\ \\ Exercises:\\ //induction, termination, determinacy, divergence// | | |
| | 10 | | | | | 08 - Partial orders and fixpoints (ctd.):\\ //recursive definitions of partial functions as logical systems, immediate consequences operator, set of theorems as fixpoint//\\ \\ 09 - Denotational semantics:\\ //lambda-notation, free variables, capture-avoiding substitutions, alpha-conversion, beta rule, conditionals, denotational semantics of commands, fixpoint computation// | {{ :magistraleinformatica:psc:2025-03-18_-_08c_-_ico.pdf |Lecture 08c}}\\ {{ :magistraleinformatica:psc:2025-03-18_-_09_-_denotational_imp.pdf |Lecture 09}} | | | 10 | | | | | 08 - Partial orders and fixpoints (ctd.):\\ //continuity, Kleene's fixpoint theorem, McCarthy's 91 function, recursive definitions of partial functions as logical systems, immediate consequences operator, set of theorems as fixpoint//\\ \\ 09 - Denotational semantics:\\ //lambda-notation, free variables, capture-avoiding substitutions, alpha-conversion, beta rule, conditionals, denotational semantics of commands, fixpoint computation// | | |
| | 11 | | | | | Exercises:\\ //posets//\\ \\ 10 - Consistency:\\ //denotational equivalence, congruence, compositionality principle, consistency of commands, correctness, completeness// | {{ :magistraleinformatica:psc:03_-_poset-2025.pdf |Exercises 03}}\\ {{ :magistraleinformatica:psc:2025-03-20_-_10_-_consistency_imp.pdf |Lecture 10}} | | | 11 | | | | | Exercises:\\ //posets//\\ \\ 10 - Consistency:\\ //denotational equivalence, congruence, compositionality principle, consistency of commands, correctness, completeness// | | |
| | 12 | | | | | Exercises:\\ //well-founded recursion, posets, semantics//\\ \\ 11 - Haskell:\\ //an overview//\\ \\ Haskell ghci:\\ //basics, tuples, lists, list comprehension, guards, pattern matching, lambda, partial application, zip, exercises// | {{ :magistraleinformatica:psc:03_-_poset-2025.pdf |Exercises 03}}\\ [[https://www.haskell.org/|Haskell]]\\ {{ :magistraleinformatica:psc:2025-03-21_-_11_-_haskell.pdf |Lecture 11}}\\ {{ :magistraleinformatica:psc:ghci-session1-2025.txt.zip |ghci session 01}} | | | 12 | | | | | Exercises:\\ //well-founded recursion, posets, semantics//\\ \\ 11 - Haskell:\\ //an overview//\\ \\ Haskell ghci:\\ //basics, tuples, lists, list comprehension, guards, pattern matching, lambda, partial application, zip, exercises// | | |
| | 13 | | | | | Haskell ghci (ctd):\\ //recursive definitions, tail recursion, let-in, where, map, filter, fixpoint operator// | [[https://www.haskell.org/|Haskell]]\\ {{ :magistraleinformatica:psc:ghci-session2-2025.txt.zip |ghci session 02}} | | | 13 | | | | | Haskell ghci (ctd):\\ //recursive definitions, tail recursion, let-in, where, map, filter, fixpoint operator// | | |
| | 14 | | | | | Haskell ghci (ctd.):\\ //folds, application, function composition, exercises//\\ \\ 12 - HOFL:\\ //syntax, pre-terms, types, types judgements, type system, type checking, type inference, principal type// | [[https://www.haskell.org/|Haskell]]\\ {{ :magistraleinformatica:psc:ghci-session3-2025.txt.zip |ghci session 03}}\\ {{ :magistraleinformatica:psc:2025-03-27_-_12a_-_hofl_types.pdf |Lecture 12a}} | | | 14 | | | | | Haskell ghci (ctd.):\\ //folds, application, function composition, exercises//\\ \\ 12 - HOFL:\\ //syntax, pre-terms, types, types judgements, type system, type checking, type inference, principal type// | | |
| | 15 | | | | | 12 - HOFL (ctd.):\\ //canonical forms, operational semantics, lazy vs eager evaluation// | {{ :magistraleinformatica:psc:2025-03-28_-_12b_-_hofl_operational.pdf |Lecture 12b}} | | | 15 | | | | | 12 - HOFL (ctd.):\\ //canonical forms, operational semantics, lazy vs eager evaluation// | | |
| | 16 | | | | | Exercises:\\ //Haskell//\\ \\ 13 - Domain theory:\\ //Integers with bottom, cartesian product, projections// | {{ :magistraleinformatica:psc:04_-_haskell-2025.pdf |Exercises 04}}\\ {{ :magistraleinformatica:psc:2025-03-28_-_13a_-_cartesian_domains.pdf |Lecture 13a}} | | | 16 | | | | | Exercises:\\ //Haskell//\\ \\ 13 - Domain theory:\\ //Integers with bottom, cartesian product, projections// | | |
| | 17 | | | | | 13 - Domain theory (ctd.):\\ //switching lemma, functional domains, lifting, let notation// | {{ :magistraleinformatica:psc:2025-04-03_-_13b_-_functional_domains.pdf |Lecture 13b}}\\ {{ :magistraleinformatica:psc:2025-04-03_-_13c_-_continuity_theorems.pdf |Lecture 13c}} | | | 17 | | | | | 13 - Domain theory (ctd.):\\ //switching lemma, functional domains, lifting, let notation// | | |
| | 18 | | | | | 13 - Domain theory (ctd.):\\ //continuity theorems//\\ \\ 14 - Denotational semantics of HOFL:\\ //definition and examples, type consistency, substitution lemma, compositionality// | {{ :magistraleinformatica:psc:2025-04-03_-_13c_-_continuity_theorems.pdf |Lecture 13c}}\\ {{ :magistraleinformatica:psc:2025-04-04_-_14_-_hofl_denotational.pdf |Lecture 14}} | | | 18 | | | | | 13 - Domain theory (ctd.):\\ //continuity theorems//\\ \\ 14 - Denotational semantics of HOFL:\\ //definition and examples, type consistency, substitution lemma, compositionality// | | |
| | 19 | | | | | 13 - Domain theory (ctd.):\\ //continuity theorems, apply, fix, curry, uncurry//\\ \\ 14 - Denotational semantics of HOFL (ctd.):\\ //only free variables matters, canonical terms are not bottom//\\ \\ 15 - Consistency of HOFL (ctd.):\\ //Counterexample to completeness, correctness of the operational semantics, operational convergence, denotational convergence, operational convergence implies denotational convergence (and vice versa), operational and denotational equivalence, correspondence for type int, unlifted semantics, lifted vs unlifted semantics//\\ \\ Exercises:\\ //HOFL, domains// | {{ :magistraleinformatica:psc:2025-04-03_-_13c_-_continuity_theorems.pdf |Lecture 13c}}\\ {{ :magistraleinformatica:psc:2025-04-04_-_14_-_hofl_denotational.pdf |Lecture 14}}\\ {{ :magistraleinformatica:psc:2025-04-08_-_15_-_consistency_hofl.pdf |Lecture 15}}\\ {{ :magistraleinformatica:psc:05_-_hofl-2025.pdf |Exercises 05}} | | | 19 | | | | | 13 - Domain theory (ctd.):\\ //continuity theorems, apply, fix, curry, uncurry//\\ \\ 14 - Denotational semantics of HOFL (ctd.):\\ //only free variables matters, canonical terms are not bottom//\\ \\ 15 - Consistency of HOFL (ctd.):\\ //Counterexample to completeness, correctness of the operational semantics, operational convergence, denotational convergence, operational convergence implies denotational convergence (and vice versa), operational and denotational equivalence, correspondence for type int, unlifted semantics, lifted vs unlifted semantics//\\ \\ Exercises:\\ //HOFL, domains// | | |
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| ^ N ^ Date ^^ Time ^ Room ^ Lecture notes ^ Links ^ | ^ N ^ Date ^^ Time ^ Room ^ Lecture notes ^ Links ^ |
| | 20 | Thu | 10/04 | 14:00-16:00 | C1 | Exercises:\\ //HOFL, domains//\\ \\ 16 - Erlang:\\ //an overview// | {{ :magistraleinformatica:psc:2025-04-10_-_16_-_erlang.pdf |Lecture 16}}\\ [[http://www.erlang.org/|Erlang]] | | | 20 | | | | | Exercises:\\ //HOFL, domains//\\ \\ 16 - Erlang:\\ //an overview// | | |
| | - | Fri | 11/04 | 09:00-11:00 | L1 | **Canceled due to graduation event** | | | | 21 | | | | | Erlang erl:\\ //numbers, atoms, tuples, lists, terms, variables, term comparison, pattern matching, list comprehension, modules, functions, guards, higher order, recursion, pids, spawn, self, send, receive, examples//\\ \\ 17 - CCS:\\ //Introduction to concurrency// | | |
| | 21 | Tue | 15/04 | 09:00-11:00 | E | Erlang erl:\\ //numbers, atoms, tuples, lists, terms, variables, term comparison, pattern matching, list comprehension, modules, functions, guards, higher order, recursion, pids, spawn, self, send, receive, examples//\\ \\ 17 - CCS:\\ //Introduction to concurrency// | [[http://www.erlang.org/|Erlang]]\\ {{ :magistraleinformatica:psc:2025-04-15_-_16a_-_erlang_session.pdf |erl session}}\\ {{ :magistraleinformatica:psc:2025-04-15_-_17a_-_ccs.pdf |Lecture 17a}} | | | 22 | | | | | 17 - CCS (ctd.)\\ //Syntax, operational semantics, value passing, finitely branching processes, guarded processes// | | |
| | 22 | Thu | 17/04 | 14:00-16:00 | C1 | 17 - CCS (ctd.)\\ //Syntax, operational semantics, value passing, finitely branching processes, guarded processes// | {{ :magistraleinformatica:psc:2025-04-15_-_17a_-_ccs.pdf |Lecture 17a}}\\ {{ :magistraleinformatica:psc:2025-04-17_-_17b_-_ccs_guarded.pdf |Lecture 17b}} | | | 23 | | | | | 18 - Bisimulation:\\ //abstract semantics, graph isomorphism, trace equivalence, bisimulation game, strong bisimulation// | | |
| | - | Fri | 18/04 | 09:00-11:00 | L1 | **Easter holidays** | | | | 24 | | | | | 18 - Bisimulation (ctd.):\\ //strong bisimilarity, strong bisimilarity is an equivalence, strong bisimilarity is a bisimulation, strong bisimilarity is the coarsest strong bisimulation, strong bisimilarity is a congruence, some laws for strong bisimilarity, strong bisimilarity as a fixpoint, strong bisimilarity as a fixpoint, Phi operator, Phi is monotone, Phi is continuous (on finitely branching processes)// | | |
| | - | Tue | 22/04 | 09:00-11:00 | E | **Easter holidays** | | | | 25 | | | | | 18 - Bisimulation (ctd.):\\ //Guarded processes (again, from Lecture 17), Knaster-Tarski's fixpoint theorem//\\ \\ 19 - Hennessy-Milner logic:\\ //modalities, HML syntax, formula satisfaction, converse of a formula, HML equivalence//\\ \\ 20 - Weak Semantics:\\ //weak transitions, weak bisimulation, weak bisimilarity, weak bisimilarity is not a congruence, weak observational congruence, Milner's tau-laws//\\ \\ 21 - CCS at work:\\ //modelling imperative programs with CCS// | | |
| | 23 | Thu | 24/04 | 14:00-16:00 | C1 | 18 - Bisimulation:\\ //abstract semantics, graph isomorphism, trace equivalence, bisimulation game, strong bisimulation// | {{ :magistraleinformatica:psc:2025-04-24_-_18a_-_ccs_abstract.pdf |Lecture 18a}}\\ {{ :magistraleinformatica:psc:2025-04-24_-_18b_-_ccs_bisimulation.pdf |Lecture 18b}} | | | 26 | | | | | 21 - CCS at work (ctd.) :\\ //modelling imperative programs with CCS, playing with CCS (using CAAL), modelling and verification of mutual exclusion algorithms with CCS and CAAL//\\ \\ CAAL session (copy the text and paste it in the Edit panel) | | |
| | - | Fri | 25/04 | 09:00-11:00 | L1 | **Italian liberation day** | | | | 27 | | | | | Exercises:\\ //Erlang, CCS//\\ \\ 22 - Temporal and modal logics:\\ //linear temporal logic (LTL), linear structures models, shifting, LTL satisfaction, equivalence of formulas, automata-like models// | | |
| | 24 | Tue | 29/04 | 09:00-11:00 | E | 18 - Bisimulation (ctd.):\\ //strong bisimilarity, strong bisimilarity is an equivalence, strong bisimilarity is a bisimulation, strong bisimilarity is the coarsest strong bisimulation, strong bisimilarity is a congruence, some laws for strong bisimilarity, strong bisimilarity as a fixpoint, strong bisimilarity as a fixpoint, Phi operator, Phi is monotone, Phi is continuous (on finitely branching processes)// | {{ :magistraleinformatica:psc:2025-04-24_-_18b_-_ccs_bisimulation.pdf |Lecture 18b}}\\ {{ :magistraleinformatica:psc:2025-04-29_-_18c_-_ccs_bis_as_fix.pdf |Lecture 18c}} | | | 28 | | | | | 22 - Temporal and modal logics (ctd.):\\ //computational tree logic (CTL* and CTL), infinite trees, infinite paths, branching structure, CTL* satisfaction, equivalence of formulas, CTL formulas, expressiveness comparison, mu-calculus, positive normal form, least and greatest fixpoints, invariant properties, possibly properties, mu-calculus with labels// | | |
| | - | Thu | 01/05 | 14:00-16:00 | C1 | **International labour day** | | | | 29 | | | | | 23 - GoogleGo:\\ //an overview//\\ \\ GoogleGo playground:\\ //Go principles, variable declaration, type conversion, multiple assignments, type inference, imports, packages and public names, named return values, naked return, multiple results, conditionals and loops, pointers, struct, receiver arguments and methods, interfaces, goroutines, bidirectional channels, channel types, send, receive, asynchronous communication with buffering, close, select, communicating communication means, range, handling multiple senders, concurrent prime sieve// | | |
| | - | Fri | 02/05 | 09:00-11:00 | L1 | **Long weekend** | | | | 30 | | | | | 24 - Pi-calculus:\\ //name mobility, free names, bound names, syntax and operational semantics, scope extrusion, early and late bisimilarities, weak semantics// | | |
| | 25 | Tue | 06/05 | 09:00-11:00 | E | 18 - Bisimulation (ctd.):\\ //Guarded processes (again, from Lecture 17), Knaster-Tarski's fixpoint theorem//\\ \\ 19 - Hennessy-Milner logic:\\ //modalities, HML syntax, formula satisfaction, converse of a formula, HML equivalence//\\ \\ 20 - Weak Semantics:\\ //weak transitions, weak bisimulation, weak bisimilarity, weak bisimilarity is not a congruence, weak observational congruence, Milner's tau-laws//\\ \\ 21 - CCS at work:\\ //modelling imperative programs with CCS// | {{ :magistraleinformatica:psc:2025-04-29_-_18c_-_ccs_bis_as_fix.pdf |Lecture 18c}}\\ {{ :magistraleinformatica:psc:2025-05-06_-_19_-_hml.pdf |Lecture 19}}\\ {{ :magistraleinformatica:psc:2025-05-06_-_20_-_weak.pdf |Lecture 20}}\\ {{ :magistraleinformatica:psc:2025-05-06_-_21_-_ccs_at_work.pdf |Lecture 21}} | | | 31 | | | | | Exercises:\\ //logics, GoogleGo, pi-calculus//\\ \\ 25 - Measure theory and Markov chains:\\ //probability space, random variables, stochastic processes, homogeneous Markov chains, DTMC, DTMC as matrices, DTMC as PTS, next state probability, ergodic DTMC, steady state distribution, finite path probability// | | |
| | 26 | Thu | 08/05 | 14:00-16:00 | C1 | 21 - CCS at work (ctd.) :\\ //modelling imperative programs with CCS, playing with CCS (using CAAL), modelling and verification of mutual exclusion algorithms with CCS and CAAL//\\ \\ CAAL session (copy the text and paste it in the Edit panel) | {{ :magistraleinformatica:psc:2025-05-06_-_21_-_ccs_at_work.pdf |Lecture 21}}\\ [[http://caal.cs.aau.dk/|CAAL]]\\ {{ :magistraleinformatica:psc:caal-session1-2025.zip |CAAL session 1}} | | | 32 | | | | | 25 - Measure theory and Markov chains (ctd):\\ //negative exponential distribution, CTMC, embedded DTMC, infinitesimal generator matrix, CTMC stationary distribution//\\ \\ 26 - Probabilistic bisimilarities:\\ //bisimilarity revisited, reachability predicate, CTMC bisimilarity, DTMC bisimilarity, Markov chains with actions, probabilistic reactive systems, bisimilarity for reactive systems, Larsen-Skou logic// | | |
| | 27 | Fri | 09/05 | 09:00-11:00 | L1 | Exercises:\\ //Erlang, CCS//\\ \\ 22 - Temporal and modal logics:\\ //linear temporal logic (LTL), linear structures models, shifting, LTL satisfaction, equivalence of formulas, automata-like models// | {{ :magistraleinformatica:psc:06_-_erlang_-_ccs-2025.pdf |Exercises 06}}\\ {{ :magistraleinformatica:psc:2025-05-09_-_22a_-_ltl_ctl.pdf |Lecture 22a}} | | | 33 | | | | | 27 - PEPA:\\ //motivation, basic ideas, PEPA workflow, PEPA syntax, cooperation combinator, bounded capacity, apparent rate, PEPA operational semantics, performance analysis, reward structures// | | |
| | 28 | Tue | 13/05 | 09:00-11:00 | E | 22 - Temporal and modal logics (ctd.):\\ //computational tree logic (CTL* and CTL), infinite trees, infinite paths, branching structure, CTL* satisfaction, equivalence of formulas, CTL formulas, expressiveness comparison, mu-calculus, positive normal form, least and greatest fixpoints, invariant properties, possibly properties, mu-calculus with labels// | {{ :magistraleinformatica:psc:2025-05-09_-_22a_-_ltl_ctl.pdf |Lecture 22a}}\\ {{ :magistraleinformatica:psc:2025-05-13_-_22b_-_mu_calculus.pdf |Lecture 22b}} | | | 34 | | | | | Exercises:\\ //Markov chains, probabilistic systems, PEPA// | | |
| | 29 | Thu | 15/05 | 14:00-16:00 | C1 | 23 - GoogleGo:\\ //an overview//\\ \\ GoogleGo playground:\\ //Go principles, variable declaration, type conversion, multiple assignments, type inference, imports, packages and public names, named return values, naked return, multiple results, conditionals and loops, pointers, struct, receiver arguments and methods, interfaces, goroutines, bidirectional channels, channel types, send, receive, asynchronous communication with buffering, close, select, communicating communication means, range, handling multiple senders, concurrent prime sieve// | {{ :magistraleinformatica:psc:2025-05-15_-_23_-_google_go.pdf |Lecture 23}}\\ [[http://golang.org/|Google Go]]\\ {{ :magistraleinformatica:psc:go-session-2025.zip |go session}} | | | 35 | | | | | Exercises:\\ //Samples from exam exercises// | | |
| | 30 | Fri | 16/05 | 09:00-11:00 | L1 | 24 - Pi-calculus:\\ //name mobility, free names, bound names, syntax and operational semantics, scope extrusion, early and late bisimilarities, weak semantics// | {{ :magistraleinformatica:psc:2025-05-16_-_24_-_pi_calculus.pdf |Lecture 24}} | | | 36 | | | | | Mini-projects:\\ //discussion// | | |
| | - | Tue | 20/05 | 09:00-11:00 | E | **University closed (due to Tour of Italy)** | | | |
| | 31 | Thu | 22/05 | 14:00-16:00 | C1 | Exercises:\\ //logics, GoogleGo, pi-calculus//\\ \\ 25 - Measure theory and Markov chains:\\ //probability space, random variables, stochastic processes, homogeneous Markov chains, DTMC, DTMC as matrices, DTMC as PTS, next state probability, ergodic DTMC, steady state distribution, finite path probability// | {{ :magistraleinformatica:psc:07_-_logics_-_googlego_-_pi-2025.pdf |Exercises 07}}\\ {{ :magistraleinformatica:psc:2025-05-22_-_25a_-_dtmc.pdf |Lecture 25a}} | | |
| | 32 | Fri | 23/05 | 09:00-11:00 | L1 | 25 - Measure theory and Markov chains (ctd):\\ //negative exponential distribution, CTMC, embedded DTMC, infinitesimal generator matrix, CTMC stationary distribution//\\ \\ 26 - Probabilistic bisimilarities:\\ //bisimilarity revisited, reachability predicate, CTMC bisimilarity, DTMC bisimilarity, Markov chains with actions, probabilistic reactive systems, bisimilarity for reactive systems, Larsen-Skou logic// | {{ :magistraleinformatica:psc:2025-05-23_-_25b_-_ctmc.pdf |Lecture 25b}}\\ {{ :magistraleinformatica:psc:2025-05-23_-_26_-_probabilistic_bisimilarities.pdf |Lecture 26}} | | |
| | 33 | Tue | 27/05 | 09:00-11:00 | E | 27 - PEPA:\\ //motivation, basic ideas, PEPA workflow, PEPA syntax, cooperation combinator, bounded capacity, apparent rate, PEPA operational semantics, performance analysis, reward structures// | {{ :magistraleinformatica:psc:2025-05-27_-_27_-_pepa.pdf |Lecture 27}}\\ [[http://www.dcs.ed.ac.uk/pepa/|PEPA]] | | |
| | 34 | Thu | 29/05 | 14:00-16:00 | C1 | Exercises:\\ //Markov chains, probabilistic systems, PEPA// | {{ :magistraleinformatica:psc:08_-_probability_-_2025.pdf |Exercises 08}} | | |
| | 35 | Fri | 30/05 | 09:00-11:00 | L1 | Exercises:\\ //Samples from exam exercises//\\ \\ Mini-projects:\\ //discussion// | | | |
| | End | | | | | | | | | End | | | | | | | |
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