# Questions tagged [smt-solvers]

Solver programs for the Satisfiability Modulo Theories (SMT). The SMT problem is a decision problem for logical formulas with combinations of background theories expressed in classical first-order logic with equality.

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### Which of these properties hold for all FO theories? (but not regarding fragments thereof)

Which of these properties hold for all FO theories? (but not regarding fragments thereof) a. Decidable b. At least expressive as propositional logic c. NP-complete a) Decidable: no, some first order ...
55 views

### Constraint satisfaction problem: solve system, then evaluate whether many additional constraints are satisfied one at a time

I have a system that consists of binary inequality constraints between variables, plus some indicator variables that can assume only two values: ...
190 views

### Automated reasoning with real numbers

I have a large number of equivalences which look like: $(a \leq 0.54 \wedge b \geq 0.12) \vee (c \gt 0.98)$ $\Leftrightarrow$ $(x \leq 0.25) \vee (x \gt 0.91 \wedge y \geq 0.01)$ This is just an ...
31 views

### How to leverage the fact that I'm solving 1000's of very similar SMT instances?

I have a core SMT solver problem consisting of 100,000 bit-vector array clauses, and one 10000-dimensional bit-vector array. Then, my program takes as input k << 100,000 new clauses, and adds ...
63 views

### What are the differences between symbolic execution and SAT solvers?

My understanding is that symbolic execution only deals with specific paths and bad patterns, while SAT solvers, or satisfiability modulo theories in general, provide a much more robust analysis of the ...
32 views

### Proving that a property is k-inductive with an SMT solver (parametric resettable counter)

I'm following the slides at https://homepage.cs.uiowa.edu/~tinelli/talks/FT-11.pdf where Tinelli explains how k-induction works in the context of SMT based model checking. A parametric and resettable ...
32 views

### Program synthesis based on function properties

I am fairly new at program synthesis and the use of SMT solvers for this purpose. Given a function g, I want to generate all the functions f and h such that the following holds: f . g = h . f Are ...
246 views

### Check if two items are equal after replacing

Let's say that an item is either a natural number or a list of items. Examples of items are: 1  [4, [3, 1], 3, 4] A rule states that two items are equal. For example: 1 = 2 3 = [3, 1] [4, 3] = [...
14 views

### Generating graph with complex structure

I want to generate a bunch of graphs of about 100 nodes, where each node is a categorial variable. I want the graphs to satisfy complex properties, like, "if a node of type A is connected to a node ...
131 views

### General Understanding of SMT Solving Across Multiple Theories

My first question was a little too simplified in that it turned out to be an integer linear programming problem solvable with the Simplex Method. However, what I think I am wondering about is how to ...
211 views

### How a SMT / SAT Solver Generates Valuations for this Example

First, an example of a set of constraints which turned out not to be solvable (I don't think): ...
131 views

### Passing arrays vs functions as arguments in SMT?

In SAT Modulo Theories (SMT), with the theory of uninterpreted functions, all functions are first order, that is, they don't take functions as arguments or return functions. In the theory of arrays, ...
66 views

### Objective function and constraint satisfaction over a set of multi-attributes elements

I'm looking for an approach to solve a problem consisting of maximizing an objective function over a set of discrete elements, while respecting a set of constraints. To illustrate my point, I'll try ...
1k views

### Bit Blasting Algorithm

I found a pseudo algorithm which describes bit blasting: click (page 156,157). I am trying to implement it in C, but I don't understand it yet completely. Let's make an example: Assume our bit-vectors ...
729 views

### How could an SMT solver be implemented as simple as possible?

I'm trying to figure out how an SMT solver works as simple as possible. Let's assume we have a simple input program with symbolic values x and ...
128 views

### When to use SAT vs solving?

Are there any guidelines for how to recognize, for a given problem, which approach is more likely to yield good results? SAT solver or SMT solver? Is there any guidance anyone can offer about which ...
54 views

### Verification condition in case of array theory

As far as i can understand the problem of checking safety property, can be reduce to solving for inductive invariants in VC's and there is following parts to it: Generate VC's from the program. Solve ...
134 views

### Is the optimal order of graph vertices s.t. minimizes edges to later vertices a well-known problem?

I'm a little unfamiliar with graph theory, and I found an interesting problem in my work that I do not know if its already well-known or can be easily mapped to another one. If I were to express the ...
48 views

### How the $EX(f)$ is evaluated in symbolic model checking?

I was reading the symbolic model checking, So there it has mentioned that we can represent the set of states and transition relations of any transition system with the help of ROBDDs. I was trying to ...
223 views

### Framework or tools to generate theorem prover/solver/reasoner for new logic

I have new logic which has syntax and semantics in usual natural languages and I have to create theorem prover/solver/reasoner for this logic. Is there framework or tool set that can generate such ...
141 views

### Using SMT Solvers in formula checking

I'm currently working on a static analysis work in which I need to check whether a given formula is met or not. I hope the following example clarifies my requirement. Suppose we have a list of three-...
528 views

### Exponential example for simplex used in SMT solvers

The original simplex algorithm requires an exponential number of pivot operations in the worst case, e.g., if run on the Klee-Minty example [3,4]. What about the simplex algorithm used in SMT solvers ...
46 views

So this sounds like this might lead to an undecidable theory but I thought I would give it a try and ask about it after I found nothing on the subject. I am somewhat interested in finding functions ...
278 views

### Using SMT solvers to generate random solutions to given predicate

I am interested in generating random solutions to predicates. I only need SMT for integers with the following predicates/functions <, >, <=, >=, ==, !=, +, * The algorithm I want should produce ...
153 views

### Introduction to bounded model checking that describes model generation

Most of the tutorials I have found on model checking and bounded model checking start with, the model is given as a Kripke Structure M = (S,I,T,L) where S is a set of states, I is a set of initial ...