Neil Immerman
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View article: Who Wins the Multi-Structural Game?
Who Wins the Multi-Structural Game? Open
Combinatorial games played between two players, called Spoiler and Duplicator, have often been used to capture syntactic properties of formal logical languages. For instance, the widely used Ehrenfeucht-Fraïssé (EF) game captures the synta…
View article: Multi-Structural Games and Beyond
Multi-Structural Games and Beyond Open
Multi-structural (MS) games are combinatorial games that capture the number of quantifiers of first-order sentences. On the face of their definition, MS games differ from Ehrenfeucht-Fraisse (EF) games in two ways: first, MS games are play…
View article: Parallel Play Saves Quantifiers
Parallel Play Saves Quantifiers Open
The number of quantifiers needed to express first-order properties is captured by two-player combinatorial games called multi-structural (MS) games. We play these games on linear orders and strings, and introduce a technique we call "paral…
View article: On the Number of Quantifiers Needed to Define Boolean Functions
On the Number of Quantifiers Needed to Define Boolean Functions Open
The number of quantifiers needed to express first-order (FO) properties is captured by two-player combinatorial games called multi-structural games. We analyze these games on binary strings with an ordering relation, using a technique we c…
View article: Multi-Structural Games and Beyond
Multi-Structural Games and Beyond Open
Multi-structural (MS) games are combinatorial games that capture the number of quantifiers of first-order sentences. On the face of their definition, MS games differ from Ehrenfeucht-Fraisse (EF) games in two ways: first, MS games are play…
View article: Computing Applicability Conditions for Plans with Loops
Computing Applicability Conditions for Plans with Loops Open
The utility of including loops in plans has been long recognized by the planning community. Loops in a plan help increase both its applicability and the compactness of representation. However, progress in finding such plans has been limite…
View article: New Results for the Complexity of Resilience for Binary Conjunctive Queries with Self-Joins
New Results for the Complexity of Resilience for Binary Conjunctive Queries with Self-Joins Open
The resilience of a Boolean query is the minimum number of tuples that need to be deleted from the input tables in order to make the query false. A solution to this problem immediately translates into a solution for the more widely known p…
View article: Stärken und Grenzen des Weisfeiler-Leman-Algorithmus
Stärken und Grenzen des Weisfeiler-Leman-Algorithmus Open
The Weisfeiler-Leman (WL) algorithm is a fundamental combinatorial technique used to classify graphs and other relational structures. It dates back to the 1960s and has applications in numerous fields of theoretical and practical computer …
View article: Complexity and information in invariant inference
Complexity and information in invariant inference Open
This paper addresses the complexity of SAT-based invariant inference, a prominent approach to safety verification. We consider the problem of inferring an inductive invariant of polynomial length given a transition system and a safety prop…
View article: Bounded Quantifier Instantiation for Checking Inductive Invariants
Bounded Quantifier Instantiation for Checking Inductive Invariants Open
We consider the problem of checking whether a proposed invariant $\varphi$ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can…
View article: Bounded Quantifier Instantiation for Checking Inductive Invariants
Bounded Quantifier Instantiation for Checking Inductive Invariants Open
We consider the problem of checking whether a proposed invariant $\varphi$ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can…
View article: The $k$-Dimensional Weisfeiler-Leman Algorithm
The $k$-Dimensional Weisfeiler-Leman Algorithm Open
In this note, we provide details of the $k$-dimensional Weisfeiler-Leman Algorithm and its analysis from Immerman-Lander (1990). In particular, we present an optimized version of the algorithm that runs in time $O(n^{k+1}\log n)$, where $k…
View article: New Results for the Complexity of Resilience for Binary Conjunctive\n Queries with Self-Joins
New Results for the Complexity of Resilience for Binary Conjunctive\n Queries with Self-Joins Open
The resilience of a Boolean query is the minimum number of tuples that need\nto be deleted from the input tables in order to make the query false. A\nsolution to this problem immediately translates into a solution for the more\nwidely know…
View article: Complexity column
Complexity column Open
In 1975, Ladner proved that computational complexty is dense in the sense that if C 0 is strictly contained in C 1 , for any two complexity classes satisfying standard closure properties, then there is a complexity class C 0.5 strictly bet…
View article: Complexity column
Complexity column Open
Computer programs are ubiquitous. We depend on them more and more for crucial aspects of our lives. Automatically testing whether programs meet certain safety, security, correctness and fairness conditions is thus crucial. Logic seems to b…
View article: Complexity column
Complexity column Open
We have learned a great deal about algorithms and computational complexity over the last half century. However, the lack of progress answering certain questions has been stunning. in particular, we have huge trouble proving lower bounds, i…
View article: Complexity column
Complexity column Open
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View article: Decidability of inferring inductive invariants
Decidability of inferring inductive invariants Open
Induction is a successful approach for verification of hardware and software systems. A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safe…
View article: Decidability of inferring inductive invariants
Decidability of inferring inductive invariants Open
Induction is a successful approach for verification of hardware and software systems. A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safe…
View article: A Characterization of the Complexity of Resilience and Responsibility for Self-join-free Conjunctive Queries
A Characterization of the Complexity of Resilience and Responsibility for Self-join-free Conjunctive Queries Open
Several research thrusts in the area of data management have focused on understanding how changes in the data affect the output of a view or standing query. Example applications are explaining query results, propagating updates through vie…