In this paper we provide a broad investigation of the symbolic approach for solving Parity Games.... more In this paper we provide a broad investigation of the symbolic approach for solving Parity Games. Specifically, we implement in a fresh tool, called SymPGSolver, four symbolic algorithms to solve Parity Games and compare their performances to the corresponding explicit versions for different classes of games. By means of benchmarks, we show that for random games, even for constrained random games, explicit algorithms actually perform better than symbolic algorithms. The situation changes, however, for structured games, where symbolic algorithms seem to have the advantage. This suggests that when evaluating algorithms for parity-game solving, it would be useful to have real benchmarks and not only random benchmarks, as the common practice has been.
The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse... more The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known to be decidable and ExpTime-complete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched μ-calculus that
Automated Technology for Verification and Analysis, 2004
Abstract: We introduce and study three notions of typeness for automata on infinite words. For an... more Abstract: We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class # (that is, # is weak, Buchi, coB uchi, Rabin, or Streett), deterministic #-typeness asks for the existence of an equivalent #-automaton on the same deterministic structure, nondeterministic #- typeness asks for the existence of an equivalent #-automaton on the same structure,
We consider two-player games played on finite colored graphs where the goal is the construction o... more We consider two-player games played on finite colored graphs where the goal is the construction of an infinite path with one of the following frequency-related properties: (i) all colors occur with the same asymptotic frequency, (ii) there is a constant that bounds the difference between the occurrences of any two colors for all prefixes of the path, or (iii) all
Parity games are a powerful formalism for the automatic synthesis and verification of reactive sy... more Parity games are a powerful formalism for the automatic synthesis and verification of reactive systems. They are closely related to alternating ω-automata and emerge as a natural method for the solution of the µ-calculus model checking problem. Due to these strict connections, parity games are a well-established environment to describe liveness properties such as "every request that occurs infinitely often is eventually responded". Unfortunately, the classical form of such a condition suffers from the strong drawback that there is no bound on the effective time that separates a request from its response, i.e., responses are not promptly provided. Recently, to overcome this limitation, several parity game variants have been proposed, in which quantitative requirements are added to the classic qualitative ones. In this paper, we make a general study of the concept of promptness in parity games that allows to put under a unique theoretical framework several of the cited variants along with new ones. Also, we describe simple polynomial reductions from all these conditions to either Büchi or parity games, which simplify all previous known procedures. In particular, they improve the complexity results of cost and bounded-cost parity games. Indeed, we provide solution algorithms showing that determining the winner of these games lies in UPTime ∩ CoUPTime.
Troppo spesso la scuola appare distante dagli alunni, ancorata a contenuti che sembrano scarsamen... more Troppo spesso la scuola appare distante dagli alunni, ancorata a contenuti che sembrano scarsamente applicabili e a metodi di insegnamento che producono scarsi risultati, perch? non sono in grado di integrarsi con il linguaggio della societ? digitale in cui viviamo. Questo contributo, realizzato nell'ambito del progetto INNOVASCUOLA promosso dal Dipartimento per l'Innovazione e il Ministero dell'Istruzione, dell'Universit? e della Ricerca, propone un approccio innovativo interdisciplinare per l'insegnamento delle scienze naturali, della matematica e dell'informatica nella scuola secondaria di primo grado attraverso un percorso didattico unificato nel quale gli esperimenti di scienze rappresentano la base per applicare semplici regole matematiche e per utilizzare semplici strumenti informatici.
In scholar curriculum, the integration of contents from different learning areas has been always ... more In scholar curriculum, the integration of contents from different learning areas has been always a chal- lenging issue, but with very few practical experimenta- tions. This paper reports an experimental project of teaching natural science, mathematics, and computer science (technology education) in the first level of the Italian secondary school, by means of a common inte- grate path based on practical experiments. We show effectiveness of the conceived interdisciplinary ap- proach by means of a case study in a network of thirty classrooms of 11 years old scholars.
In scholar curriculum, the integration of contents from different learning areas has been always ... more In scholar curriculum, the integration of contents from different learning areas has been always a challenging issue, but with very few practical experimentations. This paper reports an experimental project of teaching natural science, mathematics, and computer science (technology education) in the first level of the Italian secondary school, by means of a common integrate path based on practical experiments. We show effectiveness of the conceived interdisciplinary approach by means of a case study in a network of thirty classrooms of 11 years old scholars.
The attention on the use of computer games in education (educational gaming) is quickly growing. ... more The attention on the use of computer games in education (educational gaming) is quickly growing. By investigating the impact of video games in school, researchers have shown a remarkable improvement in student engagement and motivation. Nevertheless, the effects of educational gaming have rarely been considered on a long running application and, most important, they have never been considered in the whole teaching process as a means for teachers to real-time monitor students' learning. In this paper, we investigate the use of video games associated with formative assessment to pursue the above objective. In particular, we have conceived and implemented a portal, named PlayLearn, aimed at administering online tests based on multiple-choice quizzes, by means of video games. By letting the students play, the portal helps students to learn, it evaluates them and, finally stores their learning parameters which can be used by the teachers to improve in real-time the learning process, all in a virtuous circle.
Visibly Pushdown Automata (VPA) are a special case of pushdown machines where the stack operation... more Visibly Pushdown Automata (VPA) are a special case of pushdown machines where the stack operations are driven by the in- put. In this paper, we consider VPA with two stacks, namely 2-VPA. These automata introduce a useful model to eectively describe con- current pushdown systems using a simple communication mechanism between stacks. We show that 2-VPA are strictly more expressive
The model checking problem for finite-state open systems (module checking) has been extensively s... more The model checking problem for finite-state open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinite-state systems (pushdown module checking). In this part, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system's control states and pushdown store content. We study the complexity of this problem with respect to the branching-time temporal logics CTL, CTL * and the propositional µ-calculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information.
ICALP is a series of annual conferences organised by the European Association for Theoretical Com... more ICALP is a series of annual conferences organised by the European Association for Theoretical Computer Science (EATCS), whose first edition took place in 1972. In 2006, the ICALP programme run three parallel tracks: A, focusing on algorithms, automata, complexity and games (chaired by the late I. Wegener); B, focusing on logic, semantics and theory of programming (chaired by V. Sassone); and C, focusing on security and cryptography foundation (chaired by B. Preneel). In response to the call for papers, the Program ...
The solution of games is a key decision problem in the context of verification of open systems an... more The solution of games is a key decision problem in the context of verification of open systems and program synthesis. We present an automata-theoretic approach to solve timed games. Our solution gives a general framework to solve many classes of timed games via a translation to tree automata, extending to timed games a successful approach to solve discrete games. Our approach relies on translating a timed automaton into a tree automaton that accepts all the trees corresponding to a given strategy of the protagonist. This construction exploits the region automaton introduced by Alur and Dill. We use our framework to solve timed Büchi games in exponential time, timed Rabin games in exponential time, Ctl games in exponential time and Ltl games in doubly exponential time. All these results are tight in the sense that they match the known lower bounds on these decision problems.
Game theory is a useful framework in multi-agent system verification. In this context, an importa... more Game theory is a useful framework in multi-agent system verification. In this context, an important contribution is given by modal logics for strategic ability, such as ATL , SL, and the like, which allow to describe the interaction among players for the achievement of specific goals. However, most of the attempts carried out so far have focused on specific forms of games in which strategic-reasoning aspects are glued with agent temporal goals.
The present volume includes extended and improved versions of 9 papers selected from among those ... more The present volume includes extended and improved versions of 9 papers selected from among those that were presented at the Third International Symposium on Games, Automata, Logic and Formal Verification (GandALF), held in Naples (Italy) from September 6th to 8th, 2012. The GandALF series of conferences was founded by Italian computer scientists interested in mathematical logic, automata theory, game theory, and their applications to the specification, design, and verification of complex systems. Its aim is to provide a forum where people from different areas, and possibly with different backgrounds, can fruitfully interact. Even though the idea of the symposium emerged within the Italian research community, every effort was made to characterize the event as truly international, as witnessed by the composition of the conference committees and the scientific programme.
In open systems verification, to formally check for reliability, one needs an appropriate formali... more In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between open entities and express that the system is correct no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL*, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by SL CHP , with the aim of getting a powerful framework for reasoning explicitly about strategies. SL CHP is obtained by using first-order quantifications over strategies and it has been investigated in the specific setting of two-agents turned-based game structures where a non-elementary model-checking algorithm has been provided. While SL CHP is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems.
IFIP International Federation for Information Processing, 2008
The model checking problem for open systems (module checking) has recently been the subject of ex... more The model checking problem for open systems (module checking) has recently been the subject of extensive study. The problem was first studied by Kupferman, Vardi, and Wolper for finite-state systems and properties expressed in the branching time logics CTL and CTL * . Further study continued mainly in two directions: considering systems equipped with a pushdown store, and considering environments with imperfect information about the system. A recent paper combined the two directions and considered the CTL pushdown module checking problem in the imperfect information setting, i.e., in the case where the environment has only a partial view of the system control states and pushdown store content. It has been shown that this problem is undecidable when the environment has imperfect information about the pushdown store content, while it is decidable and 2Exptime-complete when the imperfect information only concerns control states. It was left open whether the latter remains decidable also for more expressive logics. In this paper, we answer this question in the affirmative, showing that the pushdown module checking problem with imperfect information about the control states is decidable and 2Exptime-complete for the propositional and the graded µ-calculus, and 3Exptime-complete for CTL * .
In this paper we provide a broad investigation of the symbolic approach for solving Parity Games.... more In this paper we provide a broad investigation of the symbolic approach for solving Parity Games. Specifically, we implement in a fresh tool, called SymPGSolver, four symbolic algorithms to solve Parity Games and compare their performances to the corresponding explicit versions for different classes of games. By means of benchmarks, we show that for random games, even for constrained random games, explicit algorithms actually perform better than symbolic algorithms. The situation changes, however, for structured games, where symbolic algorithms seem to have the advantage. This suggests that when evaluating algorithms for parity-game solving, it would be useful to have real benchmarks and not only random benchmarks, as the common practice has been.
The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse... more The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known to be decidable and ExpTime-complete, it has recently been proved that the full calculus is undecidable. In this paper, we study the fragments of the fully enriched μ-calculus that
Automated Technology for Verification and Analysis, 2004
Abstract: We introduce and study three notions of typeness for automata on infinite words. For an... more Abstract: We introduce and study three notions of typeness for automata on infinite words. For an acceptance-condition class # (that is, # is weak, Buchi, coB uchi, Rabin, or Streett), deterministic #-typeness asks for the existence of an equivalent #-automaton on the same deterministic structure, nondeterministic #- typeness asks for the existence of an equivalent #-automaton on the same structure,
We consider two-player games played on finite colored graphs where the goal is the construction o... more We consider two-player games played on finite colored graphs where the goal is the construction of an infinite path with one of the following frequency-related properties: (i) all colors occur with the same asymptotic frequency, (ii) there is a constant that bounds the difference between the occurrences of any two colors for all prefixes of the path, or (iii) all
Parity games are a powerful formalism for the automatic synthesis and verification of reactive sy... more Parity games are a powerful formalism for the automatic synthesis and verification of reactive systems. They are closely related to alternating ω-automata and emerge as a natural method for the solution of the µ-calculus model checking problem. Due to these strict connections, parity games are a well-established environment to describe liveness properties such as "every request that occurs infinitely often is eventually responded". Unfortunately, the classical form of such a condition suffers from the strong drawback that there is no bound on the effective time that separates a request from its response, i.e., responses are not promptly provided. Recently, to overcome this limitation, several parity game variants have been proposed, in which quantitative requirements are added to the classic qualitative ones. In this paper, we make a general study of the concept of promptness in parity games that allows to put under a unique theoretical framework several of the cited variants along with new ones. Also, we describe simple polynomial reductions from all these conditions to either Büchi or parity games, which simplify all previous known procedures. In particular, they improve the complexity results of cost and bounded-cost parity games. Indeed, we provide solution algorithms showing that determining the winner of these games lies in UPTime ∩ CoUPTime.
Troppo spesso la scuola appare distante dagli alunni, ancorata a contenuti che sembrano scarsamen... more Troppo spesso la scuola appare distante dagli alunni, ancorata a contenuti che sembrano scarsamente applicabili e a metodi di insegnamento che producono scarsi risultati, perch? non sono in grado di integrarsi con il linguaggio della societ? digitale in cui viviamo. Questo contributo, realizzato nell'ambito del progetto INNOVASCUOLA promosso dal Dipartimento per l'Innovazione e il Ministero dell'Istruzione, dell'Universit? e della Ricerca, propone un approccio innovativo interdisciplinare per l'insegnamento delle scienze naturali, della matematica e dell'informatica nella scuola secondaria di primo grado attraverso un percorso didattico unificato nel quale gli esperimenti di scienze rappresentano la base per applicare semplici regole matematiche e per utilizzare semplici strumenti informatici.
In scholar curriculum, the integration of contents from different learning areas has been always ... more In scholar curriculum, the integration of contents from different learning areas has been always a chal- lenging issue, but with very few practical experimenta- tions. This paper reports an experimental project of teaching natural science, mathematics, and computer science (technology education) in the first level of the Italian secondary school, by means of a common inte- grate path based on practical experiments. We show effectiveness of the conceived interdisciplinary ap- proach by means of a case study in a network of thirty classrooms of 11 years old scholars.
In scholar curriculum, the integration of contents from different learning areas has been always ... more In scholar curriculum, the integration of contents from different learning areas has been always a challenging issue, but with very few practical experimentations. This paper reports an experimental project of teaching natural science, mathematics, and computer science (technology education) in the first level of the Italian secondary school, by means of a common integrate path based on practical experiments. We show effectiveness of the conceived interdisciplinary approach by means of a case study in a network of thirty classrooms of 11 years old scholars.
The attention on the use of computer games in education (educational gaming) is quickly growing. ... more The attention on the use of computer games in education (educational gaming) is quickly growing. By investigating the impact of video games in school, researchers have shown a remarkable improvement in student engagement and motivation. Nevertheless, the effects of educational gaming have rarely been considered on a long running application and, most important, they have never been considered in the whole teaching process as a means for teachers to real-time monitor students' learning. In this paper, we investigate the use of video games associated with formative assessment to pursue the above objective. In particular, we have conceived and implemented a portal, named PlayLearn, aimed at administering online tests based on multiple-choice quizzes, by means of video games. By letting the students play, the portal helps students to learn, it evaluates them and, finally stores their learning parameters which can be used by the teachers to improve in real-time the learning process, all in a virtuous circle.
Visibly Pushdown Automata (VPA) are a special case of pushdown machines where the stack operation... more Visibly Pushdown Automata (VPA) are a special case of pushdown machines where the stack operations are driven by the in- put. In this paper, we consider VPA with two stacks, namely 2-VPA. These automata introduce a useful model to eectively describe con- current pushdown systems using a simple communication mechanism between stacks. We show that 2-VPA are strictly more expressive
The model checking problem for finite-state open systems (module checking) has been extensively s... more The model checking problem for finite-state open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinite-state systems (pushdown module checking). In this part, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system's control states and pushdown store content. We study the complexity of this problem with respect to the branching-time temporal logics CTL, CTL * and the propositional µ-calculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information.
ICALP is a series of annual conferences organised by the European Association for Theoretical Com... more ICALP is a series of annual conferences organised by the European Association for Theoretical Computer Science (EATCS), whose first edition took place in 1972. In 2006, the ICALP programme run three parallel tracks: A, focusing on algorithms, automata, complexity and games (chaired by the late I. Wegener); B, focusing on logic, semantics and theory of programming (chaired by V. Sassone); and C, focusing on security and cryptography foundation (chaired by B. Preneel). In response to the call for papers, the Program ...
The solution of games is a key decision problem in the context of verification of open systems an... more The solution of games is a key decision problem in the context of verification of open systems and program synthesis. We present an automata-theoretic approach to solve timed games. Our solution gives a general framework to solve many classes of timed games via a translation to tree automata, extending to timed games a successful approach to solve discrete games. Our approach relies on translating a timed automaton into a tree automaton that accepts all the trees corresponding to a given strategy of the protagonist. This construction exploits the region automaton introduced by Alur and Dill. We use our framework to solve timed Büchi games in exponential time, timed Rabin games in exponential time, Ctl games in exponential time and Ltl games in doubly exponential time. All these results are tight in the sense that they match the known lower bounds on these decision problems.
Game theory is a useful framework in multi-agent system verification. In this context, an importa... more Game theory is a useful framework in multi-agent system verification. In this context, an important contribution is given by modal logics for strategic ability, such as ATL , SL, and the like, which allow to describe the interaction among players for the achievement of specific goals. However, most of the attempts carried out so far have focused on specific forms of games in which strategic-reasoning aspects are glued with agent temporal goals.
The present volume includes extended and improved versions of 9 papers selected from among those ... more The present volume includes extended and improved versions of 9 papers selected from among those that were presented at the Third International Symposium on Games, Automata, Logic and Formal Verification (GandALF), held in Naples (Italy) from September 6th to 8th, 2012. The GandALF series of conferences was founded by Italian computer scientists interested in mathematical logic, automata theory, game theory, and their applications to the specification, design, and verification of complex systems. Its aim is to provide a forum where people from different areas, and possibly with different backgrounds, can fruitfully interact. Even though the idea of the symposium emerged within the Italian research community, every effort was made to characterize the event as truly international, as witnessed by the composition of the conference committees and the scientific programme.
In open systems verification, to formally check for reliability, one needs an appropriate formali... more In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between open entities and express that the system is correct no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL*, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by SL CHP , with the aim of getting a powerful framework for reasoning explicitly about strategies. SL CHP is obtained by using first-order quantifications over strategies and it has been investigated in the specific setting of two-agents turned-based game structures where a non-elementary model-checking algorithm has been provided. While SL CHP is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems.
IFIP International Federation for Information Processing, 2008
The model checking problem for open systems (module checking) has recently been the subject of ex... more The model checking problem for open systems (module checking) has recently been the subject of extensive study. The problem was first studied by Kupferman, Vardi, and Wolper for finite-state systems and properties expressed in the branching time logics CTL and CTL * . Further study continued mainly in two directions: considering systems equipped with a pushdown store, and considering environments with imperfect information about the system. A recent paper combined the two directions and considered the CTL pushdown module checking problem in the imperfect information setting, i.e., in the case where the environment has only a partial view of the system control states and pushdown store content. It has been shown that this problem is undecidable when the environment has imperfect information about the pushdown store content, while it is decidable and 2Exptime-complete when the imperfect information only concerns control states. It was left open whether the latter remains decidable also for more expressive logics. In this paper, we answer this question in the affirmative, showing that the pushdown module checking problem with imperfect information about the control states is decidable and 2Exptime-complete for the propositional and the graded µ-calculus, and 3Exptime-complete for CTL * .
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